To celebrate the holidays in his public high school science lab, Stuart Ross Rosenthal decided he would make a "chemist-tree."

He pieced together a colorful branching array of test tubes and Erlenmeyer flasks, and a few antique chemical stock bottles, filled them with various salt and mineral solutions, and then stacked them on a stand of porcelain rings. After encircling the base with a wintry-white towel, he placed a few glistening rock "presents" under the tree and surrounded them with Bunsen burner "candles."

Then, for the all-important finale, the 18-year science teacher and lab specialist at Queens Vocational and Technical High School filled a bulbous flask with shimmering shredded copper, turned it upside down, and fused it to the top – the crowning apex of his chemist-tree.

"If people say, 'Oh, I like your Christmas tree,' I say, 'It's a chemist-tree – nondenominational," says Mr. Rosenthal, who himself is Jewish and is also a multimedia artist with a studio in Manhattan. "People can argue about religion, and they can even argue with science – but you can't argue with scientific glassware."

Rosenthal's festive classroom tree hasn't led to the kind of explosive cultural clashes that have surrounded some other efforts to secularize traditional Christmas symbols in the United States. But his use of wit and an irresistible pun to replace the word "Christmas" show the lengths that some people have gone to navigate the culture war over Christmas – and indicate that this struggle is very much alive today, especially in so-called red states.

When it comes to displays in public schools or other civic spaces, such arguments have almost become a holiday tradition themselves. But the struggle has been evolving. At one time the greeting "Happy Holidays" was gaining ground. Then "Merry Christmas" enjoyed a resurgence. Now some people, representing several viewpoints, are considering how it all adds up – perhaps with a tilt toward the "Christmas" side.

Already this year, clashes have erupted in public schools from Colorado to South Carolina to New Jersey (although they rarely, if ever, happen here in New York City). Also this year, at least two states, Texas and Missouri, have passed laws that allow public schools and government buildings to display traditional Christmas scenes and symbols unhindered, as well as use the term "Christmas" to describe annual parties or programs.

"I don't think we've worked out what it means if we are a secular society or not," says Greta Austin, a religious historian at the University of Puget Sound in Tacoma, Wash. "I would argue in some ways that the United States is not an entirely secular society."

"Who gets to claim [the] public space?" she asks. "Is it a religiously neutral place, or does democracy mean that different religious groups can get equal representation according to their numbers?"

Polls indicate that about 9 out of 10 Americans celebrate Christmas, and 6 out of 10 celebrate it as a religious holiday, according to a 2012 Rasmussen poll. Another poll found that 82 percent of Americans think at least some religious holidays should be celebrated in public schools, including 50 percent who believe all should be celebrated. And 47 percent of Americans believe there is a "war on Christmas," according to a 2012 Public Policy Polling survey.

So why does the season of peace and goodwill become so rancorous? And what are the proper limits, if any, on bringing religious imagery and references into shared civic spaces such as government buildings, town squares, and – most contentious of all – public schools?

Consider the following developments just this year:

With overwhelming bipartisan support, Missouri legislators passed a carefully worded bill that reads, "No state or local governmental entity, public building, public park, public school, or public setting or place shall ban or otherwise restrict the practice, mention, celebration, or discussion of any federal holiday" – which includes Christmas. Although Democratic Missouri Gov. Jay Nixon vetoed the bill in July, citing safety concerns, state legislators voted 114 to 45 to override the veto. The bill took effect in October.

The bill was sponsored by Rick Brattin, who in 2008, two years before he was elected to the Missouri House, went to his son's preschool to help plan what he thought was its Christmas party. But once there, school administrators told him that it should be referred to as a "holiday party," without labeling it specifically as a Christmas celebration.

"They came to the parents and said, you're not allowed to call Christmas 'Christmas,' " recalls Mr. Brattin, now the Republican majority whip. "They were getting threats and lawsuits if we even [mentioned] Christmas or anything."

This June, Gov. Rick Perry (R) of Texas signed a bill that allows public school students and staff to display religious scenes and symbols on school property – and to freely express holiday greetings. "I'm proud we are standing up for religious freedom in our state," Governor Perry said in a statement. "Freedom of religion doesn't mean freedom from religion, and people of faith often feel like they can't express that faith publicly."

In Wisconsin, a bitter skirmish erupted in October when the Wausau School District decided to limit the number of sacred Christmas songs that an award-winning Masters Singers choir could sing in its longstanding holiday program. (Such songs would not have been completely eliminated, however.) The choir director and administrators could not agree on a song list – a 5-to-1 ratio of secular to sacred songs was suggested – so the choir was forced to temporarily disband before it began its annual concert tour throughout the community. An uproar ensued, and the choir's original song list was reinstated.

A similar controversy erupted in the Bordentown Regional School District in New Jersey after the superintendent, Constance Bauer, announced she was banning religious music from elementary-school winter programs. Again, an uproar from the community forced her to rescind the decision. "In reviewing additional legal considerations and advice on this matter and the expressed sentiments of the community at large, I have reconsidered the decision on the musical selection for the upcoming winter programs so that pieces with traditional and historical religious origins will be permitted," she said in a November statement.

Public schools in Colorado and South Carolina, however, stopped participating in a program called Operation Christmas Child – run by Samaritan's Purse, an evangelical Christian relief organization, headed by Franklin Graham, son of the famous evangelist. The program has schoolchildren create shoe boxes full of candy and gifts for poor children around the world – and it includes a Gospel tract and "conversion pledge" for recipients to sign.

"Some of the kids didn't realize this was a faith-connected program," says Roy Speckhardt, executive director of the American Humanist Association in Washington. "But it certainly was. And certainly parents who did a little research on Operation Christmas Child's literature could see that the purpose of this program was to convert kids to Christianity." After some parents contacted his association, it sent letters to the schools in November, threatening legal action.

Organizations like the American Humanist Association reject the notion of a "war on Christmas," however. "We just want to see that level playing field happen throughout the year, and we don't see a reason for government to be involved in promoting a particular faith," Mr. Speckhardt says.

"I think government spaces should be neutral toward religion," he says, "and religion should be checked at the door, especially if it's public officials, with endorsement capability.

"But in public spaces in general, in commons, people are welcome to speak their minds and say what they have to say," Speckhardt continues. "They can have their displays and be religious. There are just so many public opportunities to display one's faith. Those are OK – and not just OK, but people should be encouraged to have a conversation about these issues and to share their faith, or lack thereof."

But such threats of litigation rankle conservatives, who question this secular approach.

"These threats have transformed the landscape in communities around the country," says David French, senior counsel at the American Center for Law and Justice (ACLJ), a Washington-based legal group promoting the interests of evangelical Christians. "To where now, whenever they're putting on a Christmas program or they're having a Christmas display or even discussing the matter of Christmas, it raises the specter of litigation, all of the attendant publicity, the possibility of a lost case, and considerable attorney's fees."

For conservatives in Texas and Missouri, their new laws are meant to shield public schools and districts from such litigation.

Part of the purpose of the Missouri law, says Brattin, the lawmaker, is to offer protection from lawsuits brought by organizations such as the American Civil Liberties Union or the Freedom From Religion Foundation.

"In the school districts, there [was] no statutory backing protecting them [in] celebrating, and exercising their First Amendment rights," he says. Just the threat of a lawsuit created a "chilling effect" for school administrators, who had to create guidelines and policies on school displays.

For the most part, federal courts have prohibited religious expressions in public schools. But they have been quite lenient in allowing religious songs or displays of various religious symbols – if for specific instructional purposes. In some cases, even a Nativity scene is all right if it is not the obvious focal point of a program, but is among other religious displays.

In more-diverse regions, these guidelines can actually create more-robust holiday displays. Christmas trees, Hanukkah menorahs, Kwanzaa symbols, and other exhibits are common in many classrooms in New York City, and in general few complain of such displays.

"Do I as a Jew feel alienated from Christmas celebrations?" says Rabbi Shmuley Boteach, a bestselling author and speaker who has written about Christmas controversies. "No, not at all. On the contrary, I think it's a beautiful thing that Christians celebrate their heritage. I want America to be more of a religious country, without imposing religion. But I don't think that having a Nativity scene or having a Hanukkah menorah is imposing a particular set of religious beliefs."

No doubt, a vast majority of US communities have deep emotional and spiritual connections with Christmas celebrations. And for many Americans – not just conservatives – a secular ideal for expressing religion in civic spaces simply isn't working. In fact, a certain perspective from liberal scholars rejects the idea of secularism as being a "neutral" point of view, rather identifying it as just another ideological perspective.

"The more intellectual or academic expressions of this [secular ideal] have begun to receive significant ... criticism from various directions," says Brett Wilmot, associate director of the Ethics Program at Villanova University near Philadelphia, in an e-mail. "Both in terms of the empirical evidence available – the religious don't appear to be going away – and in terms of the justifications previously offered to legitimate the advance of secularism, particularly with respect to law and politics."

Mr. Wilmot zeros in on the potential effect of a commitment to be inclusive and diverse. Such efforts "generally have led – intentionally or not – to the exclusion of religion from public life in a manner that runs counter to the desires and expectations of a significant number of religious adherents," he writes.

Adds Professor Austin of the University of Puget Sound: "Even if you empty the public square of any religious expression, you still get that this 'secular' idea, it could be argued, could be like a religion. In other words, then you create a public square in which the de facto religion is secularism."

But defenders of the secular ideal see it as a way to keep religious minorities from feeling excluded. "We don't want to have the government seem like it's favoring one group over another," Speckhardt says, "and I think that's an intuitive thing that most people can get."

For their part, scholars on the right see the Constitution as permitting any community's religious expressions in civic arenas. There is no "separation of church and state" in this common conservative reading of the First Amendment, only a prohibition against a state-run church.

"From an Establishment Clause perspective, you're not establishing a religion if people who belong to a community put forward a display that acknowledges the faith of the members of the community," says Mr. French of the ACLJ. "That's not an establishment of religion by any fair reading of that term or by the original intent of the Constitution."

Beyond these legal and academic debates, in practice many people toggle on an often vague line between the secular and religious – even as controversies erupt during this time of year.

"I stand with one foot in both worlds with respect to this issue," says Wendy Patrick, a prosecutor in the San Diego County District Attorney's Office and an ordained minister with Converge Worldwide, an evangelical Baptist conference of churches. "I'm fascinated by my fervent desire to celebrate the birth of Jesus Christ. But even in a secular world, I recognize that people who don't necessarily believe love the holidays."

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"Being a county employee, I'm also very sensitive to our guidelines that prohibit how much we can celebrate," says Ms. Patrick, who often speaks on ministering in the workplace. "But we have a Christmas tree in my unit.

"We may call our party a 'holiday party,' but I'm telling you, if you walked into our holiday party, you would think it's a Christmas party. There's a Christmas tree, there's Santa Claus, there's presents. We may not use the word 'Christmas,' but that seems to be what it is."