yes, i support abortion rights. it's about self-ownership. i'm an anarchist. it's in the core of my politics.
further, yes, polling indicates young people support abortion rights and will vote for them if the issue comes up in a referendum.
however, i think i speak for most people under 50 when i point out that the existence of birth control and condoms makes abortion as a right somewhat of an uninteresting anachronism. if you're talking about people getting raped, that's one thing, and with a few exceptions even the most conservative states allow for abortion access in scenarios where people are getting raped. yet, it's a valid question to ask.
why weren't you on birth control?
why didn't you use a condom?
answers like "we got out of hand" are technically valid, but they don't produce an emotional or empathetic response. it's become an empty rights assertion that most people support in principle but that people are increasingly apathetic about.
people have the responsibility to make smart choices in life. less and less people care about bailing people out that make stupid decisions.
if you let the issue fester long enough, every single state in the united states will re-assert bodily autonomy and abortion rights.
however, the days where this is going to be a populist issue are long past as most people are going to shrug it off and say "you got pregnant? well, it's kind of your own fault, you stupid fucking idiot. it's hard to have empathy for you, when you were too fucking stupid to use a condom.".
there are more important issues in front of most people, politically, then the issue of whether irresponsible people have access to abortion or not, even if most people do support it, in principle.