I have a two year old and often worry that I'll teach him some intuitive arithmetic technique, then school will later force a different method and mark him down despite getting the right answer. What if it ends up making him hate school, maths, or both?

I experienced this. Only made me hate school, but maybe because I had game programming at home to appreciate math with

Just expose them to everyday math so they aren't one of those people who think math has no practical uses. My father isn't great with math, but would raise questions like how wide a river was (solvable from one side with trig, using 30 degree angles for easy math). Napkin math makes things much more fun than strict classroom math with one right answer

It’s valuable to learn different techniques to achieve the same result. That’s what math is all about.

Commonly school is teaching a method. "Getting the right answer" is just a byproduct of applying the method. If you tell your kid that they should just learn the methods you teach and be dismissive or angry about school trying to teach them other techniques, that's probably going to cause some issues downstream.

Techniques of an "intuitive" character often lack or have formal underpinnings that are hard to understand, which means they do not to the same extent implicitly teach analytical methods that might later be a requirement for formal deduction.