"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.