At present, the main issue is that we each have important beliefs that we don't think we can share.

Being able to share differing beliefs has more to do with whether you can both remain civil about important things than whether you agree. I regularly and enthusiastically pick apart minute disagreements between myself and my friends, and would feel as though something were lacking if I couldn't - but we can switch topics from politics to polenta when someone gets fed up and there are no hard feelings. If you can't do that with your girlfriend, that indicates a deeper-running incompatibility than merely disagreeing on rationality. Even if you agreed on all the big issues, it would be miraculous for you to make it through life without ever arguing, and being able to argue without it having it destroy your relationship is an essential skill.