I am a Nord Vampire, yet when I talk to Galmar about joining the Stormcloaks, he thinks I'm not a Nord and says "Why's a foreigner want to fight for Skyrim?" The dialogue option "So, you only take Nords?" also comes up.
Because when you become a vampire your character is removed from their typical Race category and placed in the Vampire Race category. I'm pretty sure Galmar always says the foreigner bit to Nords, though.
Galmar will always call you a foreigner, because the dragonborn in theory is a foreigner, whether you are a vampire or not. As for becoming a vampire, yes, it removes all racial interactions, because vampires are a different race totally, apparently. This causes some problems later on (DBH questline, hint, hint)
He calls you a foreigner if you're a Nord, Imperial or Breton. He calls you an elf if you're a Dark Elf, High Elf or Wood Elf. He calls you a cat if you're a Khajiit. He calls you a lizard if you're an Argonian. He calls you an orc if you're an Orc.