Every objection I have heard here is casting the construction of this community center -- it is not a mosque-- in terms of the clash of civilizations. The objectors are all casting this as some sort of proxy in the larger "Christianity is better than Islam" battle. Read the responses above.
It doesn't matter whether you think Christianity is better than Islam. That is your right to do so. The point is that the objections are all coming from this proxy battle in your heads and therefore the objections are emotional and not rational. You are equating all Muslims with terrorists. A religion with one Billion (with a B) followers is not a monolith. You don't have to like Islam. You just have to like the Constitution of the United States.