Well, that depends on what kind of story it is. If it's a love story, well, "stalking is love" is a deeply ingrained cultural trope, the core of 70% of all romantic comedies. The guy persists in the face of the girl's denial, and is eventually rewarded for his devotion. If that's what you're used to love stories looking like, you're liable to play that out when the guy's also a girl, too. With actual guy-guy love stories, you do see that same trope too... though often with rape on top of the stalking, thanks Japan... but only when it's actually a love story. And between how ingrained the "zomg the gays are coming to pervert and damn your children" trope has been over the centuries - we used get it a lot too, Carmilla is a horror story after all - and the fact that you're much more threatening to Joe Average's masculinity than we are, y'all are still getting a lion's share of that shit instead of genuine (if crappily troped) love stories, even while we've been able to move forward a bit.
If it makes you feel any better, though, the current Gen13 treatment of Sarah is pushing pretty hard for the creepy stalker throwback. (I find it especially obnoxious in this case since Gail wrote Sarah's initial attraction to Caitlin with such absolute deftness, and Sarah getting all psycho!lesbian now and Caitlin getting so aggressively dismissive of her therefore defies their history even on top of being a gross homophobic trope.)