Accurate clothing is most important for interpreters who are portraying a particular person from the past. The visitor will take in everything about them. I firmly believe that visitors can spot a phoney. These folks are not the ones we should be worried about. We should be most concerned with the people who do not catch us in our inaccuracies.
Visitors trust the museum's personnel to be the experts.
We all have a certain public authority which they crave. They absorb sights, sounds, and smells, independently of staff interaction. Character players should be as accurate as possible for this reason. The best clothing will assist the public in successful suspension of the present. This in turn will provoke them.