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Proposition 8 in California saw members from many different church groups come together in the defence of traditional marriage.
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I think you'll get broad differences of opinion on such a question. On the one hand, two churches may work together on a project which both agree is worthwhile despite differences in doctrine on the grounds that as long as we both agree on the goal, we can co-operate. Others refuse to work with other churches that differ from them by some sufficient degree because they don't want to give the impression that they are endorsing these beliefs, or that these beliefs do not matter.
Evangelicals and Catholics have frequently worked together on the pro-life movement and on religious freedom issues. But I'm hard pressed to think of other examples.
This certainly isn't a new issue. Recall the Puritans and the Separatists in the 1600s: they had similar beliefs, but the Puritans believed that the strategy should be to reform the established church, while the Separatists said that they should separate and form their own churches.