the "reds" and "spies" words makes me think cate blanchett's character is a russian spy. remember, indy films do deal in stereotypes, not to mention it sounds like a bit of an homage to james bond.
i bet all my money on the blanchett character being a russian spy.
and, imo, mccarthy is demonized more than he deserves. he was right. the hippies were a direct result of communism spreading (and today the party falls under the terms socialist and progressive). it destroyed russia, cuba, north korea and china.
if you want to keep it firmly in the '50s backdrop and not the rewritten version from a later date, the commies and soviets are the bad guys.
as for shia's hair--it's the '50s. need i provide elvis presley, james dean, etc... pics? the duckass-haired greaser archetype is much loved and synonymous with the era. indy's son being a square leave it to beaver kid just wouldn't be half as entertaining. i, personally, love the look. too bad shia's sideburns weren't a bit longer--then it would be perfect.
plus--do remember that george lucas made a little movie called american graffiti. spielberg once told terri garr that viva las vegas was one of his favorite movies. they have much love for the americana of that era (and the surrounding eras). it is a bit like spielberg getting to direct his '30s "anything goes" glittery dance montage sequence in temple of doom.