A lot of people suck at parenting which is obvious for everyone but them. Listening to some advice would help them but usually it's the attitude you present that prevents it.

Here is one example: if your kid tries to sabotage you into buying drugs (sweets) in the middle of the supermarket by throwing a tantrum you don't cave. It's simple and obvious yet so many "just don't give me advice" parents are unable to process and apply it rationalizing why they are in very special situation and no one else could possibly understand. They go and buy more drugs to their already overweight sugar addicted children just to get some temporary relief contributing to child's demise in the process.

My only advice is to try not to be self-righteous, but this has nothing to do with parenthood.

The difference is that everyone who has kids has known what life is like with and without kids. The opposite is not true.

This is true for lots of things, though, many much more exclusive than parenthood, why is having kids singled out?

And you shouldn’t speak as if you have first hand experience on those things either.

Would you take the advice of a childless pediatrician?

Absolutely. Parenthood and child medicine are very different things.

I could advise someone not to jump off a bridge even if I didn't build it.

that would depend a lot on whether they never had children or had children that died at a young age

Medicine doesn't quite work that way in the modern world.