Almost nothing can be delineated in the manner you are suggesting and that includes wealth. As such claiming that ethnicity can be ignored from a privilege perspective is simply not true.
In the US Mexicans would not be classed as white:
https://en.wikipedia.org/wiki/Race_and_ethnicity_in_the_United_States
Education.
A real understanding of genetics and how race is a social construct would be the starting point as it the cause for a massive amount of confusion.
An understanding that as humans we all carry bias, much of it subconscious, why we do this, how we can deal with it and what it means, and contrary to what Ben Shapiro claimed as a strawman it doesn't automatically mean people are racist (or sexist, homophobic, etc.).
It also can change, its not that long ago that Italian immigrants to the US were treated in a similar way to how Mexican immigrants are today.
https://en.wikipedia.org/wiki/Anti-Italianism
No it would be better that people were educated about it.