Dax, you've gotten several replies and all of them are valid. I will reply, too.
First: Freemasonry is a fraternity for men who believe in God. Because of that association, many people think that we must, therefore, be a religion. That, of course, is far from the truth: when I was young (lo, so many years ago!) a boy had to profess a belief in one of several approved dieties to become a Boy Scout. Did that make Scouting a religion? Of course not, but some people held then (and still do as far as I know) that Scouting was/is a faith. The same is true for Freemasonry.
Second: because our membership comes from a wide and divergent basis of faith, we pray to the Great Architect of the Universe (or the Supreme Architect, etc.) This, of course, is partly because we don't want to alienate any of our membership. We say, "Pray to whatever God you choose, but let's call Him the GAOTU here so that nobody is offended." Unfortunately, this offends some people (anti-Masons).
Third: We are a society with secrets (as opposed to being a secret society). The fact that there are things we will not tell the uninitiated challenges the elders (etc.) of certain faiths. They believe that they should be privy to everything from any part of their believers lives. Therefore, they see the 'secrets of Freemasonry' to be a direct challenge to their moral authority, and so, these faiths forbid their members to join us.
Fourth: there are faiths out there which forbid their members the society of those who do not belong to their church/faith/society. We hold that all believers in whatever deity share in a common truth. We do not discriminate (for the most part) on the basis of faith. Here in Wisconsin, I am told that there are Wiccans, Christians (Protestant, Catholic AND what-have-you), Jews, Moslems, Gnostics, and many other faiths represented in our fraternity. A faith which limits the society of its adherents would find this a direct challenge to their moral imperative.
Fifth: The Masonic fraternity has held for countless generations that our membership should NOT rise to the challenge and debate with those who oppose us. This basically translates to mean that anybody can say anything they want to say about Masonry and we will just be silent. This makes it easy for those out there who must have an enemy to point at us. They can say whatever they like, make us the devil incarnate in the minds of their followers, and we remain silent.
And if five wasn't enough, there are dozen and dozens more reasons that certain religions/political groups/etc oppose us.
Hope this gives you some insight.