If you don't give anyone permission to view IPs, nobody will see them (not even staff), but not logging them at all will only screw you if you get into legal trouble. I hope you know what you're doing.
Couldn't you just modify the core code and where it writes the IP address to the database, just write something else in its place? I know it's not very elegant and non-upgrade friendly but possible the simplest/quickest hack.
I'm interested to know how you can combat spam when you allow guest posting, anonymously and without IP logging. Seriously, how do you stop it and how to you block persistent spammers? Do you have staff on-line 24/7?
I think that this should be a public consumption thing - I have seen lots of requests for anonymity. I don't think it would be that hard for XenForo to have this feature built in - and of course it'll be disabled by default.
If they banned 127.0.0.1 you wouldn't be able to register/login when you are on root access to the server - but let's face it, that's not going to happen very often (you could just change it to something else like 127.0.0.100).
I agree with James. If his suggestion works then he is answering the OP's request with something that is just a config file edit. Surely that is the point of a support forum, and leave it to individuals to decide whether they want to use something at their own risk? I've seen many things posted that are equally or more destructive if done wrong.
As general rule we "purge" our IP logs every so often at random times (1 - 2x a year) (in the database).... So I can sympathize in part. We do it for optimization (it does speed up the site), security, and because many of our members change IP's anyways (often)..... However we do still keep some kind of record.