Whenever someone says "I find <word> offensive" I take them at face value, but I ask them what word I should use instead. If they have an answer, and if it really does mean the same as the other one, is commonly understood, etc., I will accommodate their wishes.
Does your friend have an alternate turn. "Someone who is not trans" would be unacceptable because it's an explanation, not a word and make speaking about it awkward. If he makes up something like "foofgender", that's no good as well, since it's not commonly understood.
If someone doesn't want me to use a term but can't come up with a substitute, they are S.O.L., as far as I'm concerned.