This is interesting, as I grew up for the first portion of my life in the US, and the majority, highschool and onwards, in China. In the Us, being white was a non-issue, as you say, it didn't matter.
In China or Asia on the other hand, it's a massive part of my identity, as are being blonde and having blue-eyes. I feel like no matter how close culturally I get, many friends saying I'm quite Asian, I am never and will never be a full part of the society I live in, and it pains me, because I love it.

Jokes and identification for me revolve around my skin colour and stereotypes of whites, hell in high school one of the cliques was simply "the white people". Fortunately those stereotypes and discrimination in Asia can be quite positive, such as everyone simply assuming I'm rich and therefore wanting my attention, or being treated better or preferentially by businesses or restaurants. My family would be purposely seated at windows of restaurants so other passersby could see that hey look, white people eat here, it must be good! At the same time, I've often encountered being thought of or referred to as "stupid white person". Being white, and even moreso having an American accent, means that I'm regarded as someone brash, ignorant, superior, and culturally insensitive. I can get away with things other Chinese can't, either because I'm white so they don't want or care to deal with me, because the issues of race discrimination, or because people just think "oh, stupid white person being an asshole, typical". No one expects me to act in a consistent manner with their culture, and are surprised and sometimes condescending when I do, as if congratulating a child on brushing their teeth.

This kind of day-to-day discrimination can be disheartening, but as I said there's a dual nature to it in Asia. When it comes to a professional setting, being white makes me more desirable, I would likely be picked over any non-white candidate of equal qualification. It's something that, while I think is silly, I would still fully take advantage of, as I assume any others in such a situation would do.

This is getting much longer than originally intended, but originally I simply wanted to point out that while I think what you said is true, I think that it's quite specific to America, and applies much less so to even Europe, and that as a function of this question, I think it's interesting to see what it might be like to be white in a non-white country. Otherwise it might be equivalent to going to an African country and asking what it's like to be black, it likely wouldn't be something that's really a "thing".