Well, is there’s no API, people complain that it’s too closed. If there is an API, people complain that it’s too open. If you don’t want AI to see and use your data, don’t post it publicly. Attaching a license or terms could make clear what can and cannot be done with the data, but enforcement will be hard.
My opinion is that having an API is preferable, because anything that is put out there publicly can already be scraped anyway, but an API makes 3rd party clients and other integrations possible, which is a good thing.
There is a solution but everyone rants about it to: DRM. The problem is it’s been used in a way that no one likes and thus says it’s evil and restricted. But in this case it could be used to limit who can do what with the data. Granted there are always ways around it like the analog loophole
I don’t believe DRM is the solution here, since it’s the public posts that are being scraped. Those public posts are by default visible by everybody, so scrapers can’t be stopped with DRM, unless you want to make a platform that can only be accessed by trusted applications.