If the user requests a resource from your server you need their IP address in order to respond to the request. So no, I don't think it's possible.

You might be able to put a CDN like Cloudflare between you and the user, and perhaps you can configure the CDN such that it doesn't forward the user's IP address, but then they would still get the IP address. That's probably not what you want either.

The next best thing might be to just scrub your server logs of IP addresses.