I mean I wouldn't want an alt-righter working at a business of mine because I'd be worried about Jewish and minority employees. It's a completely valid concern.
Alt righters are not the only people who have a chance that they may commit violence. You could have a suspicion that anyone you work with could be violent. Believing in an extremist ideology does not mean you will commit violence in most cases. In fact, if you deny alt-righters the ability to get an income, then you make them more likely to be violent because you make it impossible for them to climb the economic ladder through legal means.
It's not just about violence, which is a pretty rare thing even with those types. You just can't have a positive business culture if you have employees who hate other employees or some of your clients. Not wanting to have racists/sexists/homophobes at your business is a perfectly valid concern and not just motivated by wanting to "punish" people for certain opinions.
Do you seriously think some hardcore stormfront-esq racist would provide equally good customer service to a black customer? Of course not, thus they're an inferior employee to someone who would.