At this point, hiding from OpenAI and Anthropic is almost as hard as hiding from Facebook and Google. It doesn't matter if you personally Just Say No, when you have no way to control what everyone else in your circles will with your information.
For example, when you exchange phone numbers with someone, you don't know what apps on their phone have "contacts" access. Every fucking social media app they use now knows your name, phone number, and at least part of your social graph.
With AI, let's say you send someone an email. You have no idea what their email client will do with that. Microsoft won't fucking quit with AI integration. And even if they're using decent software that doesn't automatically funnel everything into AI, otherwise-sane people paste fucking everything into ChatGPT themselves. You cannot realistically protect yourself if you collaborate with anyone.