In the big scheme of things it doesn't matter if a mosque, church, or temple of any kind is built near ground zero.
It's easy for a few nuts in a group to cause everyone to hate or distrust the whole group.
If 9-11 had been the work of a local terriorist much like Timothy McVeigh the guy behind the Oklahoma City bombing and he was somehow affiliated with a Baptist or Christian church,..etc There would be no issue with another Christian church being built near ground zero.
On paper our country states we believe in the separation of church and state and ascribe to the belief that each of us has the right to practice whatever religion we choose.
Much like "Freedom of Speech" we often don't agree with what someone says and yet we know it's best for all of us to be allowed to express our thoughts in a free world.
The real reason there is a stink about building the mosque is because we (as a nation) have grouped all muslims into one catagory because of the acts of a few.
Once again if the vast majority of this nation was comprised of muslims and we were attacked by one of our "own" we wouldn't hold it against our group at large.