I feel inclined to answer this but please take what I say worth a grain of salt:

First, I'm also not entirely convinced that the issues you've mentioned will disappear with hierarchy and capitalism. While I think some of the most evil facets of lolicon and shotacon (physical acts of a pedophilic nature, etc.) will be dampened by a general understanding that hierarchies in relationships need not exist, I don't think this will stop people from being creepy. But I also think there are some assumptions that you're making in your post here, different from what others have pointed out.

Even in a system such as our own with centralized education, there's absolutely no guarantee that everyone in the world would agree about the morality of these things. I'm not gonna say names or point fingers, but even here in this thread there are people who would defend the act of only looking at drawings of children in sexual contexts which personally, I do not agree with at all. Looking at drawings of children is akin to actual children being portrayed in sexual contexts and thus is extremely abhorrent. Seeing someone partake in this action would lead me to believe that the motives of such an individual would be highly suspect. My point overall here though is that you can't guarantee either that people would agree on this subject entirely with a form of centralized education.

Secondly, much of what you've said here very much seems to come from a viewpoint where authoritarianism is required and built-in to solving the problems you've laid out. But I take issue with this. You're assuming that authority has to be used to tackle these issues, and I don't think that's the case. I guess this leads me to "What do we do about it all?" I'm gonna preemptively say that I don't have all the answers, nor do I think any anarchist does, but building temporary means of power, especially ones that inherently form to disband once the power is no longer needed, could be a viable solution to these sorts of issues. I prefer to think of anarchism on local scales: if a community (a neighborhood, for example) collectively agreed upon identifying individuals and deemed this an important issue, then I think they would be able to deploy means by which they could identify these individuals (reporting on these individuals to the entire neighborhood -- whether by word of mouth or posting posters on infrastructure -- and asking others to steer clear) or somehow help by having an intervention-type of meeting where all members of the community sit down with the offending member. These are just examples of temporary power that I can think of off the top of my head, but certainly other communities, who would have the time to put their heads to the issue might be able to come up with different ideas. Ultimately, it should be up to communities to decide these issues for themselves and how best to approach solving them.

I'll sum up by saying this: If we want to solve issues after we've absolved capitalism and statehood, we have to also consider how statehood and capitalism tried to (often ineffectively) solve these issues as well. We have to rethink the idea that solutions to societal problems necessitate authority or power. Maybe even means of temporary power and hierarchy are too problematic to solve these issues, we really won't know until we've tried. And so I say we should try, rather than guess at how the issues might be solved.

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I hope this addressed everything and maybe gave you a different look at how things should be viewed under an anarchist light. Maybe I've gotten something wrong here, I'm open to learning, so I hope those who disagree with me in some way will talk gently but also candidly with me about where I might have gone wrong.