Remind them you're young and at the age where many people are trying to figure themselves out. Most likely someday she will mature and not care so much about following a trend or label and even if she always choose to be "goth" that it's the person she is that you like, not her choice of style and such.
who is going to marry her, u or ur parents? I think you have to tell them this! But if you know that this is so much critical to them, and that they will feel bad for this and if you are not much fond of her just a gf u like! Then my thought is: leave her for the sake her happinness too! She will always feel odd and excluded especially at family occasions and feasts! Ask ur heart, discuss it both together and then decide it both together!
You need to let them see your girl friend as a person not a Goth Girl. How do you do that - that's the question - and I have no idea how ya do that.
Can't really blame your parents. I myself find them a bit intimidating too.
I have no clue, but you could tell that to your parents. I never understood dressing like that, but a friend of mine did. She was very artistic.
Maybe start with that Goth is a music genera.