Poverty and economic disadvantage of POC are an obvious affect of 100s of years of oppression and has kept generations of Americans in poverty.
POC are more likely to be poor, far less social mobility, less housing opportunities (loan access as an example), hurt by gentrification, lacking quality education and so much more. Over policing + horrendous and an unfair criminal 'justice' system locking up black and brown kids (this chart is so disgusting [1]) and that's if they don't get shot during a traffic stop or selling lose cigarettes.
LGBTQ face similar hurdles, triple down Trans POC who are killed at a shocking rate with no repercussions most people don't care they are disposable in their eyes.
To your example of poor whites supporting this oppression I don't have data but I have seen this in part of my extended family who live in the south. Systemically poor, no social mobility. Despite being dependent on the social safety net they are hardcore MAGA and overtly blame POC and immigrants as the reason they are poor. One uncle (long story family problem trying to get him housed) refuses to live near black people...
The problems associated with poverty and economic affect both minorities and whites. However, racism adds an extra layer of difficulties on top of the more general problems---and poor whites are some of the strongest supporters of this extra layer. Further, racism has been a problem longer than (the current wave of) poverty and economic inequality. (See, for example, the 1950s and 60s when inequality was lower but racism was much stronger.)
Edit: A corollary of this: the "problems associated with poverty and economic affect both minorities and whites" can be seen as a way to distract attention from the very real problems of racism.