Lots of people grow up and graduate from college without any education in personal finance. Ignorance of financial topics and genuine irresponsibility are not quite the same thing. Some people with bad money habits wise up at some point and take control of their finances and some of them don't. Some people get away with bad saving and spending habits because they earn a lot of money. Some people don't earn enough to get ahead no matter how careful they are. There is a wide range in awareness, behavior, and circumstances.
You need to raise the issue of finances at some point, have some serious, respectful conversations, and see if your girlfriend is inclined to turn over a new leaf. If she can adjust her habits going forward, then the existing debt may not seem so daunting. If she is really fiscally irresponsible by nature, then she might not change and might resent the suggestion that she should. But perhaps she already knows that she should be saving more and paying down debt and she would like to make some adjustments. Maybe she will welcome the impetus to start that process.
Think about how to raise the issue respectfully and take some time to work through it together. If those conversations lead to agreement on your priorities for the future, then you may evaluate your current (combined) financial situation and decide that it's not a dealbreaker. On the other hand, if you can't come to an agreement, or at least a compromise, on financial priorities for the future, your different viewpoints are the issue more than the actual debt.
My wife was not a saver when we met. She didn't have any debt, but she spent most of the money that she had. We discussed every important topic we could think of before we got engaged, including money, and agreed that saving for general peace of mind and a timely retirement was a top priority. She hadn't thought about long-term financial planning before and didn't know much about it, but she was willing to think about it and take the appropriate steps. Fifteen years later, we are in good financial shape. She is still not quite as frugal as I am, but we are generally on the same page and we are saving more than enough for our future.
Your hope is that you can continue this relationship, marry this woman (at the appropriate time if things continue to go well) and continue to feel financially secure. You need to take your time and tread cautiously, but there may be a decent chance that you can do both.
Good luck.