The whole point of reporting the incident is that it's HR's job to track and decide whether this is a one-off rant or a pattern of public homophobic behavior, n

The whole point of reporting the incident is that it's HR's job to track and decide whether this is a one-off rant or a pattern of public homophobic behavior, not the OP's. Say he doesn't report this incident and then it happens again two months from now. Is he then supposed to go to HR and report both incidents at once?! In that case, it's definitely the person's job on the line, whereas if HR gets notified the first time, perhaps they get a chance to warn the individual before they step over the line too many times.