That's possible, and it's difficult to disentangle class and race in the US, due to historical racism economically repressing many minorities. However, follow on studies to the famous resume name-swapping study found that the original study used stereotypical lower-class black names as its pool of stereotypical black names. When stereotypical lower-class white names and stereotypical upper-class black names were added to the randomized pool, a larger component of discrimination fell along class lines vs. race lines, for both white and black prospective interviewers.
I hope our discrimination problems fall more along class lines, because that's much easier to solve by implementing economic policies to reduce economic inequalities. Government programs won't change people's races (well, non-terrifying government programs, at least), but policies can change people's economic class.
It's also entirely possible that different areas of the country have different mixes of classism and racism. My wife is of a different race, and our son is mixed race, and my wife and I both went to top-tier schools, so my social group is almost certainly less racist and more classist than the US median. It's very difficult and dangerous to extrapolate my lived truth to the whole nation.