That speech is expressing an awesome idea: Juliet is saying that she loves Romeo-the-person, but she is terrified of her bad luck in that he happens to have a certain surname ("Montague") which will automatically cause her family to hate him. Which, indeed, they do. It's basically something like "why did I fall in love with such an inconvenient person?", together with "why does my family care so much about this thing that I'm not sure needs to matter?".
Sure, but the archaic language can obscure the awesome idea. "Why are you Romeo?" may sound less poetic to modern ears, but isn't that how people back then would have parsed it - just as easily as everyday language, because it was their everyday language?
I feel like in a way we're losing Shakespeare's intended effect, because we insist on using a "language" that isn't used anymore. Yes, I understand that it's considered the same language, but a language isn't really one thing, it's more of a spectrum without sharp edges. Shakespeare is much closer in time to Middle English (which is considered a different language) than he is to our time