Depends on why they don't wear it. The books are, to my knowledge, fairly unclear on this. If they truly object to the idea of metal armor, then probably not (but then, why are they so willing to travel with others who use it?), but if it's just a matter of allowing their powers to work, then they probably won't care if their animal companion wears metal armor or not. I suppose it's up to the DM as to why they're prohibited.