Well, surely you don't mean that the people receiving the bad messages should have to read them, because of course you agree that they don't have to look at twitter at all. But, why would it be important to require them to see these in order to see other posts on twitter, if they only want to see the other ones.
So, I don't see what the problem would be in providing the users with an opt-in filter option. If they are concerned that it could put them in a filter bubble, they could just not enable it, and if they are not concerned about the possibility of a filter bubble, and find the bad messages unpleasant, they could enable it. This would all just be following user choice.
Yes, if the features you give people for filtering messages are set up in certain ways, they may make it a bit easier than would be best for users to create filter bubbles for themselves, but it would at least be the user's own choice. As long as someone who wants to not get in a filter bubble can reasonably avoid it, then it seems like that's good enough on that front to me.
edit: Ideally, I think, the user would be able to fine tune the filters that they choose to use, and the simplest options would be such that they do not cause much of a filter bubble. But I think to really respect user freedom, allowing the user to create a filter bubble for themself (perhaps using 3rd party tools) is maybe necessary?