“Loathsome” and “hair shirt” are typical criticisms leveled by those in the camp that disdains non-iron shirts. These purists see the wrinkle-free versions as villains—think “Invasion of the Body Snatchers,” recast with uncomfortably rigid and stifling clone-shirts hijacking the existence of classic button-ups. “I loathe them,” said George Hahn, a writer who blogs about menswear. “Men who’ve only worn these Franken-fabric shirts don’t know the difference,” he sniffed.

A product of the Eisenhower era, a period that also spawned nonstick fry pans and frozen TV dinners, non-iron shirts debuted at Brooks Brothers in 1953. Menswear historian and author Bruce Boyer noted that chemicals conglomerate DuPont worked with the menswear retailer to launch the first generation of Dacron-and-cotton shirts. Since then the non-iron formula hasn’t changed much, other than the fact that most are all-cotton shirts rather than blends: The anti-wrinkle properties are derived from a chemical treatment that releases formaldehyde and bonds the strands of cotton fibers to create a stiffer fabric less likely to wrinkle.

“While the process makes for a wrinkle-free shirt fresh out of the dryer, the fabric breaks down and leads to blown-out elbows, becomes less breathable and feels stiffer,” said Paul Trible, co-founder and CEO of Ledbury, the Richmond, Va.-based luxury shirtmaker. “These shirts are not only bonded fibers, but have fused collars, cuffs and plackets,” said Mr. Boyer, which makes them immobile compared with traditional shirts. “Who wants to look like a sheet of aluminum?” he added.

“As everything moves to being more environmentally friendly, these artificial shirts seem out of step,” said Greg Broom, founder of MixCraft, a New York juice-drink brand. Mr. Broom likes his cotton shirts the same way he prefers his fruit juice: pure and pressed. “Wearing formaldehyde, the chemical used in embalming, has never sounded tempting to me,” he said.

Why We Love Them

It’s difficult to appear buttoned-up in your button-down when it looks as though it was exhumed from King Tut’s tomb. You might say non-iron shirts have liberated men from schlumpiness. “Non-iron shirts are a reliable way to avoid looking like a crumpled mess,” said Tim Kelly, a regional operations manager at Douglas Elliman real estate in East Hampton, N.Y. For men like Mr. Kelly, who want to be dressed in under 15 minutes, having a wardrobe of crease-free shirts at the ready reduces the hassles of the morning routine.

Non-iron shirts have also made pressing, steaming and expensive laundering services almost superfluous. “These shirts are easy as pie,” said Thomas Lavandosky, a senior project analyst with an investment firm in Los Angeles. “I hang them up right out of the dryer and don’t have to think about them. There’s no bag of button-downs to haul to the cleaner.”

(Not) Pressed for Success These crease-flouting shirts are reliably classic in design From left: Non-Iron Oxford Shirt, $90, bananarepublic.com; Non-Iron Dress Shirt, $92, brooksbrothers.com; Wrinkle-Free Shirt, $45, llbean.com; Wrinkle-Resistant Trofeo Shirt, $375, Ermenegildo Zegna, 212-421-4488 Photo: Marko Metzinger for The Wall Street Journal (3), F. Martin Ramin/The Wall Street Journal, Styling by Anne Cardenas

But that doesn’t mean that fit, texture and color are no longer concerns. At Brooks Brothers, non-iron varieties currently account for 90% of the overall shirt volume, said Guy Voglino, vice president brand manager, men’s & boys. You’ll find check versions with spread collars, triple-stripe and tattersall button-downs and three different fits. When asked whether formaldehyde is still a key ingredient in their manufacture, Mr. Voglino, like other non-iron makers who were interviewed, would only say a “proprietary formula is used, one that meets global safety standards” for both those involved in the production of them and for those actually wearing them.

Men also call out the advantage that shirts remain crisp for work and travel. “Non-irons ensure you look presentable all day,” said Eugene Ree, senior director of men’s design at Banana Republic, who favors the brand’s Grant style, notable for its tailored fit. Joe Mc-Glynn, head of new business for New York marketing agency Wunderman, praises Mizzen + Main versions that rely on a stretchy polyester spandex to keep creases at bay. “I can crumple the shirts up in a ball and still put them on without a wrinkle,” he said.

The success of non-iron shirts has inspired a high-end phalanx of “wrinkle-resistant” analogues from Ledbury, Thomas Pink, Eton and Proper Cloth. There’s no ‘proprietary formula’ to fuse fibers together: At Ledbury, for example, fabrics are sprayed with a mild solvent (Proper Cloth uses an ammonia-based spritz) and dried to stiffen the fibers before the shirt is made. Ermenegildo Zegna just launched its Trofeo shirt in fabric woven with extra-long cotton fibers that it claims delivers a smooth look. It does if your idea of smooth is flexible enough to include the mild rumpling it exhibits when you wash and hang it to dry.