I am Cherokee. I learned WHITE AMERICAN cliche silent movie culture from my racist assimilationist father. He insisted all his children were WHITE. HE called his grandmother A SQUAW. USA is misogynist patriarchal gun culture. I was given a 2 holster gunbelt with 2 cap pistols for my 4th xmas 1956. I learned natural healing cures fishing hunting gardening canning vegetables and climbing our fruit trees as a small child. I learned white jesus blue eyes prEyers from my mother. She tried to get me to call my kindergarten teacher COLORED. MY Black skinned teacher taught me love. I have rebelled from the White xian culture 63 years now since I was 5....no matter how red my Brothers skins got I was told White is pure black is greasy scary jungle bunny bad.... USA culture is defined by racism militarism sexism and consumerism. I married a woman born in Africa and my mom did not ask what country she only feared a woman named Ruth could be BLACK....most countries "culture" is self defined by race and sex..... words are "feminine" and "masculine "....I was never told a single Cherokee word or song. My father called his uncle John Matthews a "rattlesnake" my daddy word for Atheist. He died at age 96 just a mile from his sister my grandmother AND I WAS NEVER INTRODUCED TO HIM ...WHITE USA culture is exclusionary. Not a melting pot but a crucible of conquest

An outsider's view but here are my 2 cents.
I find it strange that there is such a divide in the US. I expected there to be an American culture (one that, of course, varies a bit because of geographical location or religious affiliation), but people categorize themselves into such specific groups and forget about what unites them. Instead of just being American, you must a white or black American, etc. I think that's the wrong mindset.
You can't define or identify "white"cultures because it doesn't exist. I view it as you saying there is a "blond"culture or a "tall"culture". All of these are physical descriptors and have nothing to do one's ethnic or national background. For instance, Norwegian culture and Serbian culture are different, yet a white, blond, tall person could be either or, and they would obviously not have the same culture. And let's say you are an American with ancestors from one of those countries; your experience growing up would also be different.
Also, the US is seen as a melting pot, but there are some things all people share all around the country that you could argue are cultural. Individuality, like you mentioned, is one. The way Americans interact with strangers, their open and friendly manner (which sometimes is seen as fake) could also be something cultural.
I'm curious, if you can identify certain aspects of American culture (exclude race completely) what would they be?

Consider dropping the "white" term. American culture is becoming ethnically mixed with every inter-racial marrage....in a few decades I'm projecting a blend of all colors and ethnicities.

But the "American" culture is real.

It is unique.

We have been at it a long time.

What stratifies us more is not so much color any more, but degree of success...and not necessarily educationally tied success. There's lots of money out there with folk who didn't do so well in school...but found their way in to a lucrative business.

That's why there's lots of wealthy folk out there that don't seem to be too smart.

And that's also why there's a lot of college graduates - very academically sharp - working at grocery stores and other jobs that require little or no brain power.

That seems to be the "America" I know.

I just think human history is a mixed bag of lots of really good things, really bad things and ordinary things. The focus is unfairly put on white culture. I think the reason for that is post-colonial guilt armed with the benefit of aspiration and self-effacement that white culture developed over history. I think Tom Holland would express it as our view of ourselves judged by our Judeo-Christian cultural heritage but expressed in Enlightenment terms.

Freedom is a strange word, can you define it in the American white culture?

Why the struggle? Do you intend to teach the WA culture?

After a period of political combat in my middle forties, I realized that “something” in me was seeking better health and used the political arena for the struggle. I’m now 89 and wondering if something in you is using the arena your post describes for a like purpose.