"Girlie" comes across as condescending. It's not anywhere near a slur, but it's a way of putting a woman into her place. Try calling a grown man "boy", and it's probably along the same lines, except with a tinge of sexism.
Tommy is from a different age. That stuff used to be acceptable, and change hasn't completely come for everybody. It doesn't make Tommy a bad person, it doesn't mean he doesn't respect women or that he's a chauvinist, etc. However, when reaching for an insult, he picked one that he should have stayed away from.