It's really hard (for me, and I imagine, for everyone else) to not put myself into my views and opinions. Like, when someone shows me that I'm wrong, it's natural for me to feel attacked, instead of just taking it as a learning moment. Noticing when this happens and working with it has been my main struggle in learning how to be more rational. Those views and opinions really don't need to be a part of what I consider…
> Allowing multiple beliefs to overlap This doesn't seem very rational. If your beliefs are in conflict and you're content to not resolve that, then pretty much by definition you're accepting a logical inconsistency. If resolving the intersection doesn't lead to a new stable belief system, then aren't you basically going with "whatever I'm feeling that day"?
Dealing with contradictions in our own beliefs (paradoxes) is a part of life. The rational approach is to accept that and "fuse" those beliefs carefully, not (a) accept one and reject the others or (b) avoid the topic entirely.