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My friend who used to work at a ren faire says it’s a lazy overdone joke and the people who do it tend to be dicks.
I think if you’re going to go as a trek person they need to be in full renaissance clothing to not break the prime directive, but they can have pointy side burns.
And a tricorder that they occasionally check while trying to look sneaky.
It might not be an away team, but instead they got thrown back in time type of situation, which in that case they would just have their normal outfits.