Seems to fit the definition of racial stereotyping, so yes. You have to understand that if we follow the technical definition of racism, then not all racism is malicious.
You can find many varying definitions of racism, there isn't any individual authoritative technical definition. Most if not all of them do explicitly include or imply prejudice, which is actually critical.
Here's the thing: if you're going to get on people for using language that could offend people regardless of technical then you should also acknowledge that the term racist has very loaded connotations to most people. You can't argue that calling people savages is racist because it could have been used with prejudice towards someone's race but saying people like Isaiah Dolezal are promoting racism is innocuous because it's technically true. Saying someone is being a racist will probably more often than not offend them and be viewed as harsh criticism.
You have a source for that quote by the way?
She actually says it's from one of her sons. It's unclear if that means the brother she gained custody of or her actual biological son (born to a black father), but this is the quote:
"One of my sons yesterday (told me), 'Mom, racially you're human and culturally you're black.' I do know that they support the way I identify. And they support me."
http://www.cnn.com/2015/06/16/us/washington-rachel-dolezal-naacp/index.html
Here's a black journalist that supports the culturally black sentiment:
She shouldnt have lied, and of course she cant really be black. But if she wants to be culturally black, why cant she?
http://www.thedailybeast.com/articl...zal-says-she-s-black-she-s-black-sort-of.html
Putting aside whether or not any racial stereotype should be called racism, I think you're being WAY too dogmatic about language if you think referring to a "black culture" is a stereotyping black people. It's saying that there's a strong correlation between being black and having a particular culture, one that's mostly limited to black people. It's not saying that
I'm Jewish, but I only say that because my parents were Jewish and I've genetically inherited some recognizable Jewish phenotypes, but I there isn't an awful lot about how I live my life that's very identifiably Jewish. So in other words, I'm basically using the term as a race, albeit one with far weaker differentiators than how people generally refer to being black. If someone hates me solely for being Jewish I would consider that racism, unless they're basing that hate on incorrect assumptions of my lifestyle. I'm not "culturally Jewish" at all, but I'm not at all offended by a concept of "Jewish culture." Should I be?
Are you saying this school administration's list is somehow applicable to you or me?
I think most of it is as applicable to the teachers as it would be to you or me. If you shouldn't say something to a child you're teaching because it's probably not going to be something that's okay to say in any other context.