Clothes and accessories

Their clothes merge with their skin. Only having observed from a distance and out of doors, they don't realise that clothes and accessories are not part of the human. Or, more likely, it's simply too difficult to shape-shift clothing on top of a body - there must be a join somewhere but where?

They will be caught if they ever have to undergo any kind of search or medical investigation.

Customs officer: Can I have your bag for a moment ma'am?

Shapeshifter: Erm ... I'm afraid it's er glued to my hand. I'll have to hold on to it while you look"

Customs officer: Not a problem. May we just check your shoes?

Shapeshifter: Umm ...

Customs officer: Glued?

Shape shifter: Yes.