Liberals always confuse the Constitution with what the government can and cannot do with what citizens can and cannot do. The Constitution limits the government. Citizens have every right under the Constitution to oppose and protest the building of that mosque.
It comes from their belief that all encompassing government is the end-all, be-all of how the world should be run. They don’t see people as individuals - to them we are all just groups. Massive, faceless mobs that need to be led.
The fact that the Constitution specifically enummerates what the government can do and specifically says all other things go to the States or the People is completely lost on them. That just does not fit their big government uber alles world view.