Intellectual property law covers patents, copyrights, trademarks, and trade secrets. I'm not a lawyer, but as far as I can tell there is no legal bearing on any other type of intellectual property. The closest application might be a copyright if you've fixed the character in a tangible medium (such as a written history). But even copyright law allows derivative works such as fan fiction, and an imaginary discussion, such as participation in an RPG where you collectively imagine things about an imaginary character, doesn't even begin to infringe on copyright rights.Imaginary characters in a game don't meet any definition of intellectual property that I can find.
I don't think the legal argument has a leg to stand on. The only possible argument I can see to honor such a request is that of being considerate to someone you care about and has strong feelings about something. That's perfectly reasonable! But as other people have pointed out, this opinion seems unusual enough, and it seems to be strongly held enough, that if you are playing with strangers you should really bring it up at the beginning.