Blocking GPTBot in robots.txt is a legitimate choice if you do not want your content to train models. It is separate from search: ChatGPT finds and cites pages with another crawler, OAI-SearchBot.

So the usual combination is possible: block GPTBot and allow OAI-SearchBot. What does not help is a blanket rule that blocks “anything that sounds like AI”, followed by wondering why you do not appear.

Other providers also separate training from search: Anthropic with ClaudeBot and Claude-SearchBot; Google with Google-Extended, which does not affect your presence in Search.