Since the 1920s, most Christian denominations have grappled with where they sit on the fundamentalist–modernist spectrum. More Wikipedia articles: [1] [2] [3] [4] [5]
Note that American Christians are more conservative relative to some other religious groups. For instance, Jews can be split into several large groups — Orthodox Judaism, Conservative Judaism, and Reform Judaism — and Reform Judaism generally accepts LGBT people. In America, 35% of Jews identify as Reform, while among Israeli Jews, 3% identify as Reform. In Western European, people are much more accepting of LGBT folks than Americans are (though this statistic includes both religious and non-religious Western Europeans). Elsewhere, Canada and Australia are also more accepting of gay people than the US, again regardless of religiosity.
Specific issues / theology: [LGBT] [pacifism] [ecumenism] [inculturation]
Specific denominations: [1] [2] [3] [4] [5] [6] [7] [*1]
Other related organizations: [1] [2]
Some resources that give voice to the modernist side of things:
