Yeah, they have the right. In the U.S., they have the right to say: "In your face, infidels! Allah Akbar!"
In the Middle East, the Muslims erect mosques on the sites of their victories/conquests. Doesn't that tell you something about why they have chosen that New York location?
However, don't other groups have the right to open Jewish delis next door? How about a Honey Baked ham shop and/or a ham and eggs breakfast diner that drifts delicious pork, bacon, and ham aromas toward the mosque? How about opening a strip club and a gay bar across the street or next door? Massage parlors. Live chicken sales stores. (To keep their women pure, many Moslem men relieve their tensions with chickens. And then there are debates within Islam as to whether such violated chickens are "halal" or not.)
Oh, wait, the Christians will object to the strip club and gay bar because there is also a Catholic church nearby. (Zoning restrictions limit strip clubs and bars to a minimum distance away.)
In your face, ALL you religious wackos, Muslim AND Christian.
BTW, if and when the mosque is built, there will be suppliers and workers required. Let's see how much Christians continue to object when they are offered business and jobs.