Work Disagreement Between Other Co-workers : Taking Sides?

Okay, we are a small group of ladies in our 30s working Sunday school at our church. Two of the women have had huge disagreements over EVERYTHING. Things like the kids should all have snack all at the same time or let the kids eat as they want to. Or play time should be for 20 minutes or let the kids play for as long as they want. Basically, one woman is very structured and the other is super laid back. Well, their constant disagreents have created so much tension that the rest of our group is beginning to hate coming to work. Anyway, the manager has called a meeting to take place Tuesday so all this can be hashed out. My problem is that 1 of the 2 ladies that always fights has asked me to stick up for her. I dont know what I want to do. I do want the petty bickering to stop because it does make it suck to come to work, but at the same time I dont want to olay the "sides game." I think I should ultimately keep my mouth shut and mind my business, but that probably wouldn't change the working environment. But to take sides? That might make me just as petty as they are, right? I used to love going to this job, but now I feel like a referee at a boxing match every Sunday. It sucks.