It's probably easier to spot if you're older because absolutely everything in that movie screams reference to past cultural artifact. So you'd be looking for that in every detail. A younger person would be more likely to take the plot elements at "face value", as original or as standard story tropes.
That said I was around 15 at the time I saw it so recent history probably had a lot to do with it. AIDS was in the news a lot more in the 90s.