If you want to regain the pseudo-privacy of physical spaces online, put your community’s conversations behind an authentication barrier and disable full text search of conversations.
Search engine indexing is what turns a pseudo-private space into a humiliating-public one.
It’s okay to let search engines index your forum’s existence, the sub forums it contains, and their descriptions. But do not let them index participants or conversations - either by subject, by participants, or by content. And do not offer full text search of post content to authenticated members. It’s okay to index keyword tags, but that’s it.
If you do this, you will regain the semi-anonymity that made the early Internet possible to enjoy. If you don’t, you will continue to suffer the trolls and abuse that full-text search enabled in the mid-90s (see also DejaNews, X-No-Archive: Yes, and Google’s purchase of DejaNews).
EDIT: If you truly feel that full-text search is so valuable that it must not be withheld, you have to do a lot of things to defend against abuse attackers - for example: charge money for search credits, deduct credits when they choose to reveal the text of results, warn users that their searches will be monitored for abuse, require users to be in good standing with paid membership and posting activity for at least 90 days, etc. Otherwise trolls will just use stolen cards to perform full content searches to identify users to harass and then report their findings back to a central forum. They may still do that after all the above criteria, but they’ll have to work excruciatingly hard at it. Yeah, they could manually scrape the site, but you can defend against that too (“you’ve participated on 12 days, so you’re allowed to view 12 days of old content” is a good simple test).