Thinking in absolutes is dangerous and anti-intellectual, that's the whole problem here. Rabidly following an ideology where you will entirely dismiss a person because their privately held beliefs don't align with yours.

There should be context to all decisions making. If the person has extreme views and, most importantly, they are very vocal about it to the point you don't think they'll fit into the culture of your organization, then I see no problem with not hiring them on that basis.

But at the same time if the person is able to treat others respectfully, not force their views on others, and keep personal life and business separated, then I don't see the problem with hiring them regardless of their views.

I'd be more concerned hiring a moderate democrat/republican/green/etc who forced their views on other people on the job, than hiring someone holding (what mainstream society considers) extreme views[^] and rarely talks about it at work.

[^] Note: calling for violence and coercive behavior is another story.