First of all everybody on the planet uses prejudice, research is clear that we judge if somebody is a viable sexual partner in the first few seconds with lot of work unproportional to that few seconds that can be undone but we judge them on a shallow basis.

Now that is on a individual level yet group identities of course play into that, too. And of course we are all sexist. Because to be sexist according to the definition you don't have to believe that one sex is superior to another, that they are biological differences that lead to different likely live wishes, what then is called gender roles, which the definition itself denies basically the idea that meaningfull differences about gender roles or "stereotypes" could be true.

Now you can say, but it's only 99% of women that don't want to work as engineer not 100% therefor it's unfair to generalize, well but we need stereotypes to take shortcuts and operate in a state of not full information.

If I have to make a bet about what job a female has and I assume she is not specifically selected to be the big counter example to make a point I will not bet money on she is a roofer or electrician, I will probably say something like nurse. And through my use of "sexism" I much more likely get the better outcome to win the money. And I can come up with better examples where prejustice leads to more positive outcomes, mostly because it saves time and it's easier and less time consuming to interfear and correct somebodies prejustice than not use a pattern matching algorythm in your daily live and ask 100% of people if they fit the pattern when 90-99% do. Now sure it's good to be aware that this patterns are not failproof and you should very open to correct your prejustice but start from that is not generally evil/bad, evelotion build humans with that mechanism because it was advantage to further your genes. Just because prejustice can also lead to bad/horrible things it's just a tool not more not less. And generalization are again just a tool not bad or good just neutral how you use it is important.

So back to why older people have more prejustice and vote more right wing, which goes hand in hand, because the left hates prejustice and generalization they want only hyperfocus on the exception and shame the majority often.

The point is to be inclined to believe in or even see generalization it takes time. Humans are designed to recognize patterns, the more time goes on the more time people have to notice this patterns, if they see strong patterns play out 99% of the times or 95% of the times for 1000 times they believe stronger in that to be true than if you only see it play out 50 times in your live. Therefor it makes sense to have a stronger believe in this patterns, and that this pattern is not just 1 or a few anekdote and random luck.

Popular believe seems to be that they just were raised in a different time therefor they learned by their extremly racist and sexist parents wrong things, that current culture knows better, no the same today left wingers even radicals huge amounts of them will become either more center or right wing in the future.

So to sum it up prejustice is a biological function that has a evolutionary purpose and using that has advantages and disadvantages, and case by case it's a difficult calculation if it's used negatively or positively and because older people have more data they can see this patterns that are true for most but not all people more clear, therefor they trust that seen pattern more.