Insofar as “Modernity” refers to the culture and belief system arising out of the so-called Age of Enlightenment in Europe in the 18th Century; emphasizing reason, rationality, humanism, and the marginalization of religion in social and political affairs;when the Kuffar ask “is Islam compatible with modernity?” what they really mean is, “Is religion compatible with modernity?” And by “modernity” what they really mean is rationality, reason, and moral relativism
They have no real doubt about whether Christianity is incompatible with “enlightenment” values. It is essentially an irrational and pagan belief system, and has been in continuous decline ever since the Europeans decided to emphasize intellectual reasoning. They have more or less defeated Christianity; therefore, only Islam remains a challenge to their secular materialism.
The problem for them, however, is that Islam cannot be refuted by intellectual reasoning and rational thought; on the contrary, Europe first learned of reason from the Muslims. The more they try to emphasize reason, the more Christianity fades and Islam spreads. They inherited reason and rational thought from us, but never learned how to use it properly. Because they were using it to attack a fundamentally irrational belief system, they imagined that reason is incompatible with religion; forgetting that they learned it from religious Muslims.
The same intellectual values which they have used to erode Christianity inevitably promote Islam. This has caused a conundrum, which they are struggling to solve by once again sabotaging rational thought through popular media and the culture of mindless consumerism