There's been lots of talk about whether Christianity is Avodah Zara.
Are there any distinctions between denominations, say which ones have more statues?
A building could become prohibited from benefit if it was constructed to house an "idol." Thus it was ruled a century ago that a Methodist church, which does not house any "idols", could be bought by Jews and converted to a synagogue (or any other use for that matter). This isn't a question of theology, it's one of whether there's a physical object in the building that looks like an "idol." Whereas a Catholic Church or further still, an Eastern Orthodox one ... could get a lot trickier.
Similarly, all sorts of questions were asked during WWII about saving one's life by claiming to be a Christian. One responsa discussed the potential difference between wearing a cross (just a t-shape) and a crucifix (which has someone on it).
As ArielK noted, Unitarians pose the least issues. As such Rabbi Yehuda Herzl Henkin permits one to enter a Unitarian church.