I am a little bit worried, for sure. But I think that's small extra risk on my side, for small extra gain for me personally, but large extra gain for the wider group I belong to (ultimately - all of humanity) in the sense of working towards ameliorating the "tragedy of the commons".
On the personal side. Given the LLM-s have not got the ground truth, everything is controlled hallucination, then - if the LLM tells you an imperfect version of my email or chat, you can never be sure if what the LLM told you is true, or not. So maybe you don't gain that much extra knowledge about me. For example, you can reasonably guess I'm typing this on the computer, and having coffee too. So if you ask the LLM "tell me a trivial story", and LLM comes back with "one morning, LJ was typing HN replies on the computer while having his morning coffee" - did you learn that much new about me, that you didn't know or could guess before?
On the "tragedy of the commons" side. We all benefit immensely from other people sharing their data, even very personal data. Any drug discovery, testing, approval - relies on many people allowing their data to be shared. Wider context - living in a group of people, involves radiating data outwards, and using data other people emit towards myself (and others), to have a functioning society. The more advanced the society, the more coordination it needs to achieve the right cooperation-competition balance in the interactions between ever greater numbers of people.
I think it's bad for me personally, and for everyone, that the "data privacy maximalists" had their desires codified in UK laws. My personal experience in the UK medical systems has been that the laws made my life worse, not better. Wrote here https://news.ycombinator.com/item?id=45066321