I think the pertinent question you have to ask yourself here is: Do you believe that this person will be able to competently do their job given that their politics do not align with the company's? That's really the only thing that matters, whether or not this person will do the thing you're paying them to do, at the expected level that you are paying them to do it. The rest doesn't matter, unless you make it matter.
Part of answering this question is how public the company's politics are. Does your company make it publicly known that their politics lean a particular way? If so, then it is probably reasonable to assume that this applicant knows about your politics and doesn't care; they want to work for you and do their best job despite your political differences (or they could be up to something nefarious, but I'll leave that aside for the moment; without knowing you or them I'm not going to jump to such a conclusion. I merely wanted to make note of it). If this is the case, it seems logical to me to conclude that this issue is your problem, not the applicant's problem, and that your company (or perhaps you in particular) believe this to be a dealbreaker and not the applicant.
Which itself begs the question: Are you hiring people with the skill to do the best job, or are you hiring people whose politics agree with your own (I presume you're not an officially politically-aligned organization and this is only a question of workplace culture)? You really should be doing the former; "hire and develop the best" is one of Amazon's Leadership Principles for a reason, and Jeff Bezos has the money to send his phallic rocket into space because that's how he runs his business. If your CEO wants to send his own phallic rocket into orbit, perhaps they should be more concerned with things like that rather than whether whose politics align which way. If the person joins the company and finds that he is made uncomfortable due to the politics of those around him, that's his choice to make, whether to leave at that point, but in my opinion this shouldn't enter into a hiring discussion, if you want to hire based on proficiency and not irrelevant side-issues like politics. Of course, you (and your boss) are free to disagree with my opinion, and perhaps political orthodoxy is a condition of employment at your company, which would be irresponsible in my opinion, but that's a choice you can choose to make.
Now, the above is all assuming that the applicant is aware of the politics of the company he wishes to join. That's not necessarily true, and, depending on the applicant, it may not have been a question they thought of/wanted to ask. If you have concerns in that domain, about whether the person would be a good "culture fit", you may want to volunteer this information: "At our company, we love CNN and we do whatever Master Don Lemon instructs us. Are you OK with that?", and see what he says (I'm exaggerating for comedic effect, of course, but you get the point). Perhaps he'll say, of his own volition, "no, I don't want to work for that kind of company", and that's the end of that. He may also say "you can have whatever politics you want; I'm here to do a job and make money, and as long as I'm doing those things, I couldn't care less about your politics", and then you can take him at face value (or not). But the least you can do is to make him aware of the issue and give him the choice, if he passes all your other metrics for hiring.
Here's the thing: If you assume about a person's behaviour based on their politics, well, then that's you, assuming. And you know what happens when you assume? You make an ASS, of U and ME. Don't make an ass of yourself.