Or read Butheina Hamdah, an academic, who sees alarming signs of “liberal individualism” among American Muslim women. She thinks the hijab (the Islamic head scarf) is becoming a mere “cultural marker of identity” while losing its “deeper theological dimensions.” That is why “trendy” or “sexy” versions of the hijab are emerging, she argues, while young Muslim women embrace feminist notions of “bodily autonomy” and “individual choice.”

Perhaps nothing marks this liberal trend more than the skyrocketing acceptance of gay marriage, which, as a 2017 poll showed, is now stronger among American Muslims than among white evangelical Christians. It is also reflected in the pro-L.G.B.T.Q. stance of two new Muslim congresswomen, Rashida Tlaib and Ilhan Omar. (This month, Ms. Omar took a lesson in how to integrate into America’s pluralist politics when she apologized, after heavy criticism from her own Democratic Party’s leaders, for a tweet that insinuated that American support for Israel is fueled by money from a pro-Israel lobbying group. “Anti-Semitism is real and I am grateful for Jewish allies and colleagues who are educating me on the painful history of anti-Semitic tropes,” she said almost immediately, adding, “I unequivocally apologize.”)

There are two distinct lines in this trend toward American values. One is a kind of anything-goes social liberalism, spearheaded by small groups like Muslims for Progressive Values. The other, larger line is a political liberalism that accepts a pluralist framework for society while preserving its own social and moral conservatism. Jonathan Brown, a convert to Islam and scholar of Islamic studies at Georgetown University, theorized the latter approach in a much-discussed article in which he accepted gay marriage of non-Muslims by making an analogy to traditional Muslim empires’ noninterference in what he called “incestuous Zoroastrian marriages.”

Of course, all this is happening within a political context, which Eboo Patel, an interfaith leader, explains in a chapter on “the American ummah” in his book “Out of Many Faiths: Religious Diversity and the American Promise.” In the wake of 9/11, and especially in the Trump era, Mr. Patel writes, worrying about Islamophobia has required the Muslim community to show that it really fits America. Hence, the center of gravity has shifted from “traditional Muslims,” whose authority derives from knowledge of religious sources, to a new group of media-savvy “social Muslims,” whose strength is interpreting the Muslim experience for the broader society. The interesting twist is that the progressive narrative of the “social Muslims” is having an impact on the whole American Muslim community. “Once you invoke diversity as a value,” Mr. Patel writes, it is hard to deny a place to “gay Muslims, Shia Muslims, non-hijabi female Muslims, less-observant-than-you Muslims.”

The conservatives are understandably worried that this may go too far. For example, Rashid Dar, a thoughtfully committed Muslim academic, fears the prospect of an irreversible transformation in his community. A life of “adhering to political liberalism in the public sphere but social conservatism at home or at the mosque very easily runs the risk of creating severe cognitive dissonance,” he told me. “I used to fear that this might lead to widespread ‘reform Islam’ movement s. What I fear now is widespread nihilism and apathy toward faith.”