Let's talk about the Islamic structure. There is no head, in fact, that is part of it strategy. The authority is decentralized, with religious guidance provided by diverse, independent scholars, imams.
It's fair to say there are moderates, but there are a large number of extremist "imams".

Given the following, we can now answer with a better perspective.

Incompatible with American society or incompatible wth the White Christian Nationalism that the GOP seems to be espousing?

Which mosque? Which Muslims?

What are those? Below is the stance of the many extremist Muslims; it's not just an opinion, they practice it, and expect you to practice it as well.

Lets take women/females, are they equal or subservient to men? When we look around the Islamic world, what do you see, treated as equals?
Lets take other religions? When we look around the world do the Islamic countries have large populations of other religions, or just "token" membership?
Lets take slavery? When we look around the world, what countries still have slaves (sure, sure they claim they are outlawed to get UN money, but its not enforced)?
Lets take homosexuality? When we look at the Islamic world, is homosexuality in the open?
Lets take food? Is non-halal allowed in Islamic countries?

How about blocking the roads to pray?
Call to Prayer throughout the town/city??

If Christians did this, would you have a problem?

Are these American society values? I contend they are not. Is the US an Islamic nation without the religion?

How do you know the mosque being built is moderate? Or extremist? Or is it possible to be built as moderate and turn extremist?

All of these reasonable questions the West isn't talking about. As I have stated, the West needs to neuter Islam extremism.
This will be very difficult given its proposition.
Its funny for me on the outside, as Muslims are clearly as intolerant, if not demonstrably more so, than Christians, yet the Lumpers will argue for Islam and not for Christianity.
In the end this is about the Tolerance Paradox.