False; Twitter’s algorithm pushes lots of stuff you don't directly follow and is very clearly heavily driven by subject categorization (which is often also hilariously bad), as well as stylistic categorization (or maybe instead of it, as I see very little indication that the latter plays a role.) So, if you see toxic posts, it probably means you engage with tweets ON SUBJECTS on which some people post toxic takes, or follow people who post tweets on such topics.
It doesn't require any direct interaction with toxic tweets or individuals.