I don't think the problem is the costumes, it's the Cold War mentality that informs the humor and the plot. Also the view of progress and the Future (another theme in the show) is rather "Jetsons" and not the way things actually turned out.
As for sexism, I think we can accept that as just one more aspect of the "backwardness" of Dogpatch, especially since the women are quite active in the plot. Sadie Hawkins Day is, after all, a rather feminist touch. (Worse, in my view, is the homophobic notion that men with muscles must be queer.)
But General Motors no longer rules the stock market and we don't conduct open-air A-bomb tests any more. As we've seen in the past few weeks, even the veneration of Confederate icons is on the wane. The producers of a revival would have to provide a glossary to everyone under 50.
All of which is a shame, because I would argue it has the funniest score ever written. Few musical comedies have more than one or two numbers that are truly witty. In Li'l Abner, all but a couple of ballads are hysterical!
P.S. While we're talking, what does "Don't that take the rag off of the bush!" mean anyway? The mind reels!