I don't have a problem with celebrities running for office. I think there's potentially good criticism to be made of mainstream media outlets who sometimes (not always) give too much promotion to such efforts because, you know, celebrity. But there's no reason to believe a famous actor is somehow necessarily inferior to, say, your local car dealer. And, frankly, being a senator isn't exactly a step up in the exciting department. If someone's genuinely into it, I've got nothing against it.
Sure it's NO FAIR that being famous gives you a leg up as it's no fair that being rich generally or being in a political dynasty does, but that's the way things work.
Until I have my hour long personal interview with Ms. Judd I won't be able to judge fully, but I'm reasonably sure the simple fact that she snogged Wesley Crusher makes her more qualified to be senator than Mitch McConnell. Because he's Mitch McConnell.