Consider your threat model - figure out what you want to protect against, how you can achieve it, and then decide if it’s worth it. For example if you don’t want your ChatGPT transcripts read out at your funeral, just don’t log in. Or create an account that’s not linked to your regular email / real name. If you’re concerned you’ll be identified by cookies, use an ad blocker. IP address? Use a VPN. Each measure adds a layer of privacy, but probably just using a throwaway email is enough.

Surprised no one else has chimed in with this yet - but what is your threat model? Are you conducting terrorist activities? Good luck. Are you wanting private messaging between you and your friends - it’s probably fine - definitely better than texting. I will temper this with just keep in mind anything you send to someone could be screenshot, their partner could see it etc. You need to figure out who your potential adversary is before deciding if a communication channel is “safe”. First ask yourself “safe from what?”.