How old is your girlfriend? She's acting like she's maybe late teens or early 20s...and very immature for her age.
She's asking to meet your parents. WHY?!?!?!?!?
1st) You brought up the subject of marriage, but it takes two to form a marriage. What are her feelings on marriage? Does she want to marry you? If so...
2nd) WHO does she imagine she will be marrying? You are not asking her to marry your parents. Beyond that, statistically speaking...the marriage is more likely to fail if your parents like her, too...
It is not your parents marriage that you are looking for, it is your own. For that reason, the parental units quite often (more often than not) do not approve of your choice for a marriage partner. If the parents DO approve, then it's quite possible that you are not mature enough to get married, yet. By the time you figure out what you need in a wife, for example....you will discover that the girl you need to be your life partner has like literally nothing in common with your biological mom, other than the fact that they are both women. THAT'S IT.
You ask if it's reasonable for you to be nervous at the thought of your girlfriend meeting your parents. The only reason you should be nervous is that you aren't married yet, and your future wife is already making unreasonable demands, thinking that she owns you already... (YIKES)
There is literally no good reason for your parents to meet your girl, before you marry her. Even after you marry her, it's not like your parents will be a significant presence in your new marriage. Whether your parents approve of your girlfriend or not should mean NOTHING to you. And it should mean even LESS to your girlfriend.
So what's with the power play here? I don't understand. Maybe she's just testing you like a toddler throwing a tantrum hoping to get her way, and therefore learn how to manipulate the adults...
Again, your parents don't have to approve of or even meet your future wife. And your future wife is not marrying your parents. If your future wife is insisting on meeting your parents, I would have to stop, take a step backward and wonder why?
If you cave to this demand which is unreasonable, you will spend the rest of your life doing exactly what your wife wants to do, nothing more and nothing less. A marriage should not be that way. You can share your life with someone else without losing your own free will.