Certainly everybody has a right to wear pretty much what they want - to jury duty or elsewhere.
But I have a right to think, "Jeez, what a nut."
Wearing something ridiculously inappropriate to a serious occasion such as jury duty - a Trek uniform, biker leathers, a cheerleader costume, bunny ears - would indicate to me one of two things: The wearer has no respect for the occasion or the wearer is at least slightly nutty.
If this woman sincerely believed that a Star Trek uniform was appropriate, she's a nut. Sorry, but that is how it really and truly strikes me. If this woman did it to get out of jury duty or to make a joke out of jury duty, she should have been ashamed of herself. I expect she wasn't, but she should have been.
And I agree with Arpy that including a tricorder and a phaser elevates it to an entirely new level of either oddness or lack-of-respect-for-the-institution-ness.