They notice that something different is happening. They ask if everything is handmade. They wonder how you can stand do be corseted. Historical clothing is interesting and immediate. Questions about it are good ice-breakers for shy visitors.
Museums have a public responsibility to be as accurate as current scholarship allows.
Since museums form public perception, they are obliged to do the best they can. As I said before, I think it is only desirable in certain circumstances. If the museum takes the matter on, it really should take it very seriously. Costumes are for clowns. It is insulting and insensitive to dress interpreters in costumes.