This is actually pretty low stakes in the grand scheme of things. Like, hair dye isn't permanent - worst case scenario it fades weird or they hate it after a week. I get the concern about school and future employers, but honestly most schools these days are way more chill about this stuff than they used to be, and by the time your kid's actually job hunting, the hair will look totally normal again.
Maybe the compromise is less about saying no and more about the logistics? Like, you could set some reasonable boundaries - temporary dye first to see if they actually like it, or semi-permanent so it fades faster. If their school has strict policies, that's worth checking before committing to the full neon pink. Or suggest they do it over summer break if there's pushback from their school. The main thing is probably talking through *why* they want to do it. Sometimes it's just self-expression, sometimes it's peer pressure, and knowing the difference actually matters for how you approach it.
Honestly, letting them experiment with something as temporary as hair color is way better than them feeling like they can't express themselves at home. You're not exactly ruining their life prospects by saying yes to this one.