IMO, abstract algebra is a great way to turn off all but the best of the best to math in general. I know many math majors that switched to stats and econ after floundering in the intro to abstract algebra class.
And I strongly object to trying to slip those things into early math classes; even concepts like commutativity, associativity and distributivity are simply counterproductive to students until they have some reason to need to use them in the abstract.
And FWIW, I was not personally put off by this stuff, so that's not my reason for saying this (I almost bailed thanks to calculus, though, thanks to the unreasonable focus on limits and all that garbage which any competent person can pick up practically by osmosis once they know how to actually use the damn techniques). I got quite far along in abstract math (and had the pleasure to learn some of it from Serge Lang himself, and the displeasure of fighting through the sadistic exercises in his textbooks - the guy was far more comprehensible in person!), and I absolutely love it now; however, I think it's the type of thing that a person needs to realize they want to learn about before they will be receptive to it.
On that note, I think number theory is a good soft intro to higher math, because the open problems are so easy to state and understand (3k+1, Goldbach, etc.), and you can at least see "evidence" for them using simple methods. It's hard to draw connections between number theory and the abstract stuff without a lot of machinery in place (I don't think high school students are quite ready for adeles!), but interest in those problems is what spurs a lot of work in abstract techniques, so I think it's worth nurturing.