Blocking stuff like this happens all the time. I'll give you a hypothetical, then a real-world example.
Say someone bombed a gay nightclub. Then fred phelps decided he wanted to rent a building across the street. Would the left (and the right for that matter) not go apeshit over that one? Would it not be seen as overly provocative?
Now for the real world. A couple of months back a guy in one of the small towns in missouri just east of KC wanted to open up a youth activity club. He wanted to call it "black flag." Nothing wrong with that, right? Well, it turns out that this guy is a former member of a white supremacist group and the "black flag" was the color of flag william quantrill rode under. The zoning permit was first approved, but then the people of the town--mostly white--raised hell with the zoning board and it was reversed. It was considered overly provocative among other things.
But the left will just continue to excuse radical islam. Right down to the day when a sword hits their neck, I'm sure.