I'm not sure the implication is that he's a serial rapist. Maybe for some it is though. However, for argument's sake, let's say her version of events is true. A one-time thing. Should someone that did that be on the Supreme Court? That becomes the question.
If the facts are taken most favorable to the accuser in this situation which, if I'm understanding them is: an intoxicated juvenile male, thirty-five years ago, forced himself on a girl at a party and she ran away before any sexual touching happened, and it's not part of a demonstrated pattern of misconduct. Do I think that's substantial enough to negate a judicial career? No, I don't. For a number of reasons that range from moral to legal. The greatest mitigating factor being the age and intoxication, and the statute of limitation on rape in DC being 15 years. That 15 years is for 1st and 2nd degree offenses that actually occurred, mind you. It's 10 years for lesser offenses. So we're a quarter century past anything actionable here.
Normally intoxication isn't a grant of leeway to me; however, coupled with the juvenile status is does mitigate it some. Juveniles are not supposed to partake in alcohol specifically because the ability to make judgement decisions are even more diminished. Do I think the actions of a drunk high school kid three decades ago inform how someone will act on the SCOTUS? Absolutely not.
Again, all of the above is hypothetical because you asked. I don't believe that the claim is bona fide at this time.
It may be fun, or politically advantageous, to view these #metoo claims as some kind of expedient 'gotcha', but it's an absolute perversion of justice in almost every case. No rules of evidence, no standard of review, no jury of peers; just some blathering on social media and then lost jobs and broken careers. Are some deserving? Sure. But how do you really know?