With regards to your statement "I would have an incredibly hard time believing that that person was taking me seriously, really wanted to work with me, wasn't going to undercut me, or trusted me.", in many ways I totally respect that concern.
But I also think it may be symptomatic of how our approach to these topics has become non-constructive. We've too closely tied support for a person with support for everything they do/believe. To my thinking, whether I take you seriously or want to work with you has nothing to do with the aforementioned topics, and entirely with how you behave/execute at work. And if I'm going to undercut you at work because I disagree with your beliefs, the issue isn't that I disagree with you, it's that I'd be willing to undercut anyone I work with.