Voting the way you really want in primary elections might be counterproductive.

Let's say in the main election 45% of the population will vote for whatever candidate represents side X, 45% of the population will vote for whatever candidate represents side Y, and 10% is more-or-less in the middle.

If, during the primaries, side X votes for a far-X candidate, they will definitely lose the middle 10% to a moderate-Y candidate, leading to a strong Y victory. But if side X votes for a moderate-X candidate during the primaries, the main election will be moderate-X vs moderate-Y, and they have a pretty good chance of securing the slightly-more-than-half of the middle they need for an X victory.

Of course you now end up with a lukewarm moderate X victor who isn't going to represent your far-X views, but at least you're not dealing with an even worse Y-side victor.

The real solution is to get rid of the winner-takes-all system inherently resulting in a two-party election, but Good Luck doing that kind of overhaul!

It does not stop far X candidates becoming president though, does it? Your current president is surely not moderate?

The UK has winner takes all parliamentary elections but still has multiple parties represented in it. There seem to be a lot of other barriers to other parties in the US doing the same.

Quibble: I think you're conflating "remove winner-takes-all" with "less spoiler effect". The first implies (some of) the second, but not vice-versa.

For example, ranked-choice voting would reduce the spoiler effect and allow you vote for your real choice, however it would not (on its own) change that races have a single winner, who eventually "takes all."

This matters because even if it's preferable to have both, ranked-choice is easier to introduce incrementally and with fewer amendments to various constitutions.