With publishing, from what I've seen (which, to be fair, is limited) the professional is much more personal than with, for example, managing a retail store. I mean, books are inherently personal and political, so it makes sense that there's a lot of overlap with the personal, the political, and the professional in the literary world. And as far as social media and blogs go, most people don't use them for purely professional purposes, so I believe in giving folks the leeway to talk about the things that matter to them and are happening in their lives. Being free and easy on twitter doesn't mean that they'll be unprofessional when dealing with editors or clients.
And a lot of agents and editors feel it's important to be political vocal and active, regardless of what their specific politics are. So you'll be ruling out a lot of people if you don't query those folks, so I'd definitely keep an open mind there.
For me, as a citizen, I have more respect for the agents who get political. For me, as a writer, I'm super political and my books don't shy away from social issues, so I'm more likely to click with an agent who gets that and aligns with me on the important stuff. So I make sure to query the agents that I can see care about what's going on in the world. I know there are writers who like to query agents who get personal, because they're more comfortable with those folks. So I think it's fine to figure out who you're the most excited about and comfortable with and look forward to querying those people, but don't rule someone out unless they said something that is or approaches being a total dealbreaker for you or that kind of thing. Cos you never know what someone is like in real life until you talk to them. They might be the perfect agent for you and you can just privately cringe about their facebook feed. lol
