It is not at all uncommon for girls your age to develop very intense emotional relationships with each other. What concerns the parents is defining the relationship as sexual when you are so young. It’s generally a mistake for kids your age to take any relationship to that level. It’s more important to explore what it means to have a deep and trusting friendship where you enjoy each other’s company, talk about important things, and have fun doing things together. This is how young people learn who they will eventually want to partner with.
You and your friend would show her parents how mature you are if the two of you could talk to them about voluntarily putting some limits on any sexual aspect of your relationship for now. Let her parents get to know you for the neat person you are. I hope you can talk to your parents about the situation and get some help there as well. If you are willing to go along with some limits, you might be able to work something out.
I wish you well.