[the_af]

You more or less have to assume sexual attention is unwanted in the workplace. This is merely a default, and is sometimes the wrong assumption; the problem is that the error is more serious when you assume the attention is ok but wasn't.

"But I'm polite and I'll back off if Cute Tech Support Gal isn't uninterested" isn't enough. When multiple customers decide to hit on her, this is probably upsetting to her regardless of whether you in particular were willing to back off. Even if everyone backs off it's still upsetting. It negatively impacts her work experience. Especially if her coworker, Tech Support Guy, is not constantly flirted with and customers treat him more professionally instead.

To me it's self-evident that hitting on someone using a tech support form or chat is especially lame. We're not talking about a couple who are coworkers, go to lunch frequently, talk every day, and then something blossoms between them. I've no problem with that. Instead, this is creepy male customer behavior, which decide to abruptly hitting on a staff member just because she was a girl and they liked their tiny profile picture. This really screams "inappropriate".