Shitty people exist and always will. It would be foolish of me to say otherwise. The shitty things they do may still happen in a stateless society. Child porn and slavery are being produced in societies with central government right now and very little is being done about it. In a stateless, moneyless society there would be no incentive for slave labor and I think that would largely/entirely disappear.

Child porn is obviously a lot more complex than that and there are several factors in play. First, anarchists and adjacent movement are staunch advocates of community engagement and vigilance. We want to radically change how society functions at the most base levels. If a child is being abused or exploited, it would ideally be easier to spot and act on. There hasn’t been a lot of research into what causes pedophilia or how to treat it in a way that would reduce/eliminate people acting on those urges. Research could be conducted into practical and holistic ways to treat their condition. Poverty is strongly linked to sexual violence of all kinds and the abolition of poverty would surely have a big part to play in the reduction of many things, including child sexual abuse. A society formed around the ideals of libertarian socialism present a real opportunity to end the cycle of abuse and that would certainly play a role in reducing child sexual exploitation.

There’s plenty more to say about this and there’s obviously a lot of detail not covered in my brief comment but there are solutions to this baked into the ideological framework of anarchism and libertarian socialism. I’m not going to say we have all the answers, of course we don’t. But a society organized from the bottom up, with a focus on equality, safety and prosperity for all would not only be incentivised to solve these problems, but would be much quicker to act due to the lack of bureaucratic red tape