I would say in general that this person's inability to keep these views to themselves during the hiring process is a strong indication, regardless of which side of the issue they are on, that they will bring them up, maybe repeatedly, in the office. I also think it shows lack of professional judgement on what's appropriate to discuss in a professional environment.
Therefore, they will spend time arguing and distracting coworkers espousing these beliefs and will contribute to a toxic workplace, in addition may impact other people's attention where they may then stop working to argue with this person, or find it difficult to concentrate while they bring up these views in the office.
I think as a rule of thumb, if you have learned somehow this person's extremist views, in such a short time frame, your team members will as well, and it will not be a good cultural fit.
If this happened to me... If the candidate seemed good, professionally, I would talk to them and say... Look....it's been this much time and I have been made aware you have a very divisive view on this topic. This topic has nothing to do with work. I'm interested in hiring you, but if you bring these issues up in the office, as it is a sensitive subject, it will very likely make other team members uncomfortable. I am comfortable moving forward with this but you need to be aware we have a policy against discussing politics in the office and I'm concerned, as our discussions so far have already made your views known.
Update - he mentioned in the comments it came about from social media activity and not in the workplace. Very different scenario... An argument can still be made that one needs to be careful about their social media presence as they can be interpreted as a representative of an organization, but I think this is much less severe. If he has kept it out of the office and it's only been found by scrutinizing his social media, then I think absolutely he should be able to be part of the workplace, so long as he is able to keep those views to his private life and not in the office... If it's a problem that those are on social media, maybe your company develops a policy on this and addresses it, but I think that's much less serious than my initial interpretation that this came up out of his own discussions during hiring process