"What would you do if you find that your 15 year old son has been reading manosphere and white supremacist material for quite some time?"
The same thing if I caught him reading feminists and Black Supremacist material, or any of the other extreme Leftist stuff that's commonly out there right now. I would simply inform him that he's dabbling in --ideology--, so to be careful about what he takes as truth in any of that. Then let him figure it out for himself.
I don't know what defines as "manosphere", but I do know that even the slightest disagreement with Leftist sjw's will bring charges of "white supremacist" lickety-split! They have totally de-legitimized themselves at this point. Is anybody paying attention to their -foaming at the mouth- of "racist", "bigot", "sexist", "fascist", "nazi" ??? I sure aint' !!
Reality Check: Under today's Leftist ethos, Martin Luther King would be considered a right-wing racist for not going along with the present cultural M@rxist dynamic of defining racial groups and speaking down about Whites, while demanding privileges for others. His dream specifically looked to NOT judge by race. This is the EXACT OPPOSITE of what sjw's, Leftists, feminists and all identity-politic followers do today