Sorry, no. Money changes everything. Poor whites and rich whites are not on the same side, and rarely have they ever been. You also have a startlingly short sighted view of history. History doesn't start at 1946.

Being white didn't save anyone during the Great Depression when there was no such thing as a social safety net, little to no labour laws, no government health care, and banks had free reign to impose draconian penalties and seizures of assets. Three of my grandparents lost everything they owned, my Grandfather's family was broken up (he was a D-Day vet, and gave this country the only thing he had left, his health and sanity). The only reason one of them didn't lose everything they had was due to having nothing to take away. They were all white, 3 out of 4 with British/Scottish heritage. 

Poor working-class whites have absolutely nothing to apologize 
 or feel guilty for. We'll never get the apology or reparations we are owed.