It could be one of two things. It could be that the person is deferring to the man, or it could be that since your gf is doing the talking, the person in the customer service position is trying to include both of you by acknowledging your presence also. If you had been doing the talking, maybe you and your gf would have appreciated that she acknowledged the other person in the party, which would be your gf in that situation. But, you were there, so I am going to assume your interpretation is correct, and your gf was being semi-ignored.
Interestingly, I don’t notice this happening when my husband and I are in a situation like that, I’m going to watch for it now. Maybe I am conditioned to be ignored in that type of situation and don’t realize it. Was your gf annoyed by it? Or, you noticed more than her?
What I do feel a lot of the time as a woman is that when I am alone with a service man, too often they try to tell me some bullshit, like I’m an idiot, and I think that’s at least partly because I’m a woman. Something that makes no logical sense. Those experiences of feeling less respected, or not taken seriously, happens all too often. It’s not just simple service situations, but also more serious situations like the doctor’s office.
In the situation you described, if it seemed blatantly obvious I was being ignored, I think either my husband would walk away, or possibly shrug signaling to the service person he has no clue. Or, he would say, “I don’t know why you’re looking at me, she’s the one dealing with it.” Or, I might say, “I don’t know why you’re looking at him, I’m the one talking to you.”