The lack of an ability to prevent someone from doing something to you, without compromises on your part, is not the same thing as being okay with it being done to you.

3rd party services can access the posts, because the authors marked them as publicly accessible.

Those same 3rd party services can also index the posts in a search engine, but this is only because there is no feasible technological barrier to prevent them from doing so. If such an imaginary technology did exist, it would have been deployed already.

In the mean time, we can only count on a social solution, which is to merely signal our objections to search engine indexing, in the hope that maybe a law could be drafted that uses that as precedent to make indexing without consent illegal.

Here's a question for you. Do you think it's okay for Google or whoever to install invisible cameras everywhere in public spaces, that were explicitly for the purpose of collecting data to develop a facial recognition model to search people without their consent? Public space is public space ...