Muslims have their rights, too.

Really?  Do they?  Are you saying that any group that comes to the United States can have whatever they want because it is their right?  I would say not in this case, for the following reasons:

Muslims were responsible for the 9/11 terrorist attacks.  There is no doubt about that.  Ah, but you say that was just a few extremists, and that Muslims are peace loving.  Muslims have been at war with Israel for centuries.  How is the peace thing working?  The so-called moderate Muslims have chosen not to voice  opposition to the 9/11 attacks, and polls at that time indicated 40% of Muslims were supportive.

Muslims are here looking to build a Muslim country.  They have no desire to be Americans, for Americans are infidels that deserve death.  Muslims are also making it quite clear that they have no respect for Americans or people of other faiths.  They declare that it is their right to build a mosque where ever they want, and if you don't like it, screw you!