In my experience, there is often a bit of conflict among these various groups due to relatively minor philosophical differences. However, these kind of alliances are crucial in allowing our voice to be heard. Despite our differences, it makes no sense to refuse to align with those who value the separation of church and state and oppose religion in politics.
Here's how the Secular Coalition for America described the effort:
President George W. Bush's re-election in November was a galvanizing event for many groups in American politics. Republicans, of course. Conservatives, certainly. Americans who consider religious faith a valid consideration in public policy, perhaps. But Bush's re-election also was a galvanizing event for another group: People who don't necessarily believe in a Supreme Being and who would prefer that, if there is one, he or she stay out of American politics.Keeping religious belief out of politics and government is certainly something I can support.
Of course, the problem is that efforts at coalition-building are likely to result in increased mainstreaming. Thus, there is always the danger that the real message will get lost. For example, if a militant atheist group joins up with less militant groups or moderate religious groups who also hope to avoid a theocracy, it is hard to imagine them not having to set aside their core message. This is where the conflict comes from. And yet, some compromise may be necessary to achieve a partial victory.