The Catholic Church is also in a constant state of reform. Although painstakingly slow at times the church is able to progress and has proven so in the past (ex: Second Vatican Council)
It's perfectly reasonably to have opinions that seem contradictory to your belief yet still be an active, evolving member.
Upon what basis does the Church have? The Bible is a static document that doesn't change.
The bible can be misinterpreted or translated wrong.
Religious leaders like the pope can change previous understandings
When a religion is based around a book, changing the 'understanding' of it is a farce. The next guy could just come around and change it back. At least a social movement seeks tangible, lasting goals such as constitutional amendments, or simply the rights they are entitled to. 'Reinterpretations' do not come without sufficient grounds to do so.
Logical conflict between religion and social movements?