Allying with the Cylons would be enough really. They have no reason to trust them other than lack of anyone else to trust. They all likely see the Cylon attack to be completely unprovoked after the Cylon War and possibly a Cylon plot to wipe out the last of humanity. They've gone through constant Cylon attacks for the last few years, many were likely on New Caprica and had to go through that ordeal and now some Cylons roll up with some story about a civil war and want to be friends. It would be like Hitler landing in Washington and asking for help fighting the other Nazis. They'd see it as an absolute betrayal.
You can't really blame them, they aren't working from the same knowledge of the audience where we know the rebel Cylons were the ones who didn't want to wipe them out. Plus the fact that Tigh was a Cylon and still the XO had to be rough. They knew Adama had a weak spot for Tigh, most had to be aware he is a drunk and Adama allows it. They could think that they used Tigh to trick Adama into allowing the Cylons to wipe them out.
If I were in the situation I can't say I wouldn't join in, unless I had an absolute trust in Adama's leadership and judgement.