I'm not a
Judy fan (obviously) and I do find it dated. Having said that, I do think
Judith (with or w/o a nick) definitely could work today. There was a Judith/Judy at our pool several years ago. She's about 13 now. Her family has moved to Sweden and believe it or not, I have wondered once or twice how the Swedes have embraced her name! I wonder if older names are all the rage there as well.
I visited an interesting website several years ago where people give their impressions of certain names. The general consensus of
Judy was that of a secretary yet
Judith was viewed as either an attorney or a college professor.
And yes,
Jude could absolutely work as a nick for Judith/Judy.