Natively, it's only logged when posting.
I don't know of any extension to disable this, but an easy hack would be to use the webserver configuration (example, Apache headers module) to set a proxy IP header that's hard-coded to a placeholder value, like 127.0.0.1. When a proxied IP is provided, Flarum will log it instead of the inbound IP, which can be exploited to hard-coded an IP in this case. At least I think it should work.
