Unless you're just going for light-hearted fun. Then throw them merrily in. Their incongruities give you free humor.
It's when it's trying to be grave that things cause problems. That kind of humor can only help undermine the world. I have in fact, read two stories that both deal with the -- ehem -- Good Folk. In one, most of the fairies were sourced from the British Isles, but there were peris (Persian) and kitsune (Japanese), both of whom were vulnerable to iron. Good story, but this caused a twinge. In another, it's only British fairies that suffer from iron and the church bells; Greek ones, centaurs and satyrs, do not fear iron, and a genie prays every day, to their surprise. Which left me thinking -- are they really the same thing?
If it sounds like they couldn't win for losing, that's probably right. They were both of them good stories, but it twinged. The actual folklore is a jumble. If a genie fears a Seal of Solomon, a fairy, cold iron, and a huli jing, virtuous government officials, putting in all three will be a jumble.
The only writers who have pulled multi-source folklore off, in my experience, are those who have heated it all to a melting point and let it fuse into a new form. For the vulnerabilities, I would suspect that a Unified Theory of Vulnerology would be needed, to fit together why some are harmed by some things, and some by others.