I recently watched a curious debate that took place in 2015 at the Free Press Society of Denmark. On one side was Geert Wilders, the far-right Dutch politician and anti-Islam campaigner whose ascendance to power was, I’m happy to say, checked by the elections in the Netherlands this month. On the other side was Flemming Rose, the journalist who angered many Muslims in 2005 by publishing cartoons depicting the Prophet Muhammad in the Danish newspaper Jyllands-Posten.

The crux of the debate was what to do with Muslims and Islam in Europe. Mr. Wilders argued that the Quran must be banned and mosques must be shut down. Mr. Rose, in contrast, explained that this view is unacceptably authoritarian, and Muslims deserve freedom like everyone else. “You cannot deny Muslims the right to build a mosque or to establish faith-based schools,” he said, simply because some Europeans find them offensive.

Most Muslims watching this debate would probably sympathize with Mr. Rose, thinking he was defending them. Mr. Rose, however, was merely defending a liberal principle: freedom for all. It was the very principle that led him to publish the cartoons of the Prophet Muhammad — cartoons seen by many Muslims, including me, as offensive.

This is just one of many manifestations of a paradox Muslims, especially those of us living in the West, face in the modern world: They are threatened by Islamophobic forces against which they need the protections offered by liberalism — freedom of speech, freedom of religion, nondiscrimination. But the same liberalism also brings them realities that most of them find un-Islamic — irreverence toward religion, tolerance of L.G.B.T. people, permissive attitudes on sex. They can’t easily decide, therefore, whether liberalism is good or bad for Muslims.