There a very thick line between having religious or ideological beliefs, whichever they are, and promoting or taking part in borderline criminal activities.
A potential terrorism apologist or pedophile/pervert will probably get me into trouble if I hire him. As said, it's basic business sense. Its like a dating a girl who is trash talking her previous 45 boyfriends. There's a 120% chance that you will be number 46.
Policing candidates social media is checking speech and thought. Not cool.
Radical thought: Maybe have a conversation with your candidates? Because if they are prepared to broadcast their views to the world via social media, I have little doubt about their candour in person! Not to mention dress and demeanour tend to be a giveaway.
Identitarian types are never subtle. They like to broadcast their affiliation because they are so blinded by their moral certainty and self-righteousness.
You're creating a straw man by mixing in sexual deviants with purveyors of opinions you don't like. Especially as criminal deviants will try and hide their tracks its a false equivalence with what's actually being discussed, which is a question on what the extents of free speech and expression are.
My issue is really simple: If you say its OK for employers to only select candidates they share politics with, you will end up with balkanization and inevitably ideological compaction cycles as people within the organization sense devotion to the prevailing ideology is an important indicator of status and acceptance.
Switching polarities just sets the chain reaction off in the opposite direction with the end-stage just as catastrophically unhinged.
Said it before, and I'll say it again: Sanity lies in the centre, where polar swings can happen but stay within sane and civil limits.