Jude is on a singing contest and she's dressed in silver body fitting clothes and
has put on a platinum-coloured wig.

Jude: Well I gotta go be who I am with semi-nude aliens. Does she mean her looks?

Tommy: Because nothing says legitimate singing contest like space prostitutes.
When she talks of "semi-nude aliens", could she be referring to other characters in the story? Are there other people fitting that description in the singing contest, for instance?
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Yup, they're all dressed the same way.
I can't fully explain it, I'm afraid.

"I gotta be who I am" usually means "I've got to behave in a way that reflects my personality", but exactly how this relates to being in a group of people dressed as aliens I don't know.