I really don't want to come across as someone who's just bashing the Conservatives. I genuinely was responding to the OP.
I wonder if the bullying thing is down to numbers? With Momentum (and I'm no Momentum fan), it's very large. If you join, you will encounter a vast group of people, of all ages, with a range of opinions. There will be people there who are interested in grass-roots stuff, like food banks and are, actually, pretty moderate; you'll also encounter the loud, types, who go on about Marx. It'll be an education in people, if nothing else. You'll meet lots of folk and probably gravitate towards the like-minded.
My suspicion is that the free-fall of numbers of people, especially young people, joining the Conservatives, means that there just aren't enough people to say: "No. Posting comments about euthanising chavs is not OK. It's not the level of political discussion we're about."
I'm not saying this to diss the Conservatives. It's rather to elucidate how something like that - and the bullying - can happen. And it's something you should discuss as a parent, because the discussion is clearly not happening from within the group(s).
I'd hope I'd talk to my child irrespective of whatever group they joined, to be honest.
Just to repeat: I am not seeking to run down joining the Young Conservatives (or whatever they are called at the moment). My fundamental opinion is that political engagement is a good thing generally (short of fundamentalism or extremism).
Actually, I can see I'm just digging a deeper hole for myself. I should probably stop.