As the other poster said, I think an honest framing of just what you said is fine ("I really enjoy working here, but those other things are non starters"). If it truly was not outlined beforehand, then just point out that you feel strongly enough about the extra requirements that you would not have taken the job in the first place had it been mentioned.

Maybe they accept it, maybe it becomes a learning moment for them in the future. Either way, its unfortunate but non-starters are non-starters.