Firstly, you have my respect for being a foster parent. You really do. It's a tough job I could never do.
However, I do agree with PP that you are not equipt to IAPT a child of another ethnicity. Please don't be so defensive and try to hear what people are trying to say.
Race is a very very VERY complex issue. Doing a few courses on diversity or whatever is not enough.
As a mixed race person (white and black) we do not experience the world in the same way as you. Not at all. In any aspect of life.
Race is about identity. At 13 she will be trying to discover her identity. It's already probably been ripped apart due to whatever landed her in foster care. Being mixed race in a white family will be harder than you think.
She may have said some things unacceptable, but she is probably a) hurting and very angry b) pushing boundaries deliberately because of a and c) unable to eloquently express her thoughts and feelings on race.
"I’ve asked her why she feels so passionate about her culture" - I'm sorry but this is incredibly ignorant. Why is your culture important to you?! It's her whole identity. I would definitely advise reading the books above and linking in with a black mentor/foster carer.
"Just praying this is all a faze and she will eventfully settle" - her identity is her identity and not a phase. She won't 'forget it' and it won't phase out as a topic in her mind. It's her BEING.
You need to find a way to converse with her about her race and identity but you are not prepared for that conversation evidently.
I would read the books and try to link in with someone, but to do that you have to be open and willing to explore A LOT. You (come across) to have a very defensive attitude which can be typical of some people challenged about race. Please be open and listen. PP here are right. Please mull over their comments with openness and not defence.
I wish you and this young girl luck.