That’s not how the fediverse functions
That is how the fediverse functions. Instances send posts to anyone who request it, unless a block is in place. ActivityPub is opt-out and the web has always worked this way.
be mindful of the culture
There is no "the culture" on the fediverse. Your talking about a subgroup, which has a different opinion from other subgroups. They don't get to define "culture" on the fediverse.
I don't think an admin's permission has anything to do with it. If you post publicly on the fediverse, your posts are public. You should have the option to opt out of any indexing (just like you do for the rest of the open web). But saying its ok for you to read this post if it happens to come across your feed but you shouldn't be allowed to find it via a search is ridiculous. Users get to make the choice with each post whether its public or not, but they don't get to control how people consume those public posts.