From experience in communities you can probably guess:
If someone is a right-wing shit-stick elsewhere, they'll use that bias in every decision they make & every opinion they form in every part of their life, including in your community and especially if they're given any sort of power.
It'll start out small, subconsciously, influencing how they vote on moderation decisions and how they give their 'impartial opinions' on how to handle things.
It'll then grow into direct actions and words, by which time they've already established themselves as someone who is "normally pretty impartial" and who "leaves politics at the door".
The escalating incidents will be passed off as "one-off things which I'm sure has been a valuable learning experience for everyone, regardless of their beliefs".
No.
Firmly 'kick them to the curb' as soon as you find out. Discount everything they've said and any decisions they were involved in. The temporary loss in progress and community stability is not worth putting up with the slow-acting poison people like that secrete.
Being apolitical is bullshit, and who the fuck actually wants to be neutral when it comes to human rights?