Always wondered why people “traditionally” moved right as they aged

I don't believe it has ever been seriously suggested (by serious researchers) that there's a link directly between age and conservatism. Rather, there are links between conservatism and various things that tend to be more common with age. Marriage, home ownership, higher wealth, etc. So it's unsurprising that a generation where that is happening much less would be the one where the correlation with age disappears.