At least in the U.S., poor people buy used cars, while existing and proposed ICE bans effect new car sales. Any real economic effect will be delayed until after the ban, and in any event they'll still be buying used cars. I suppose used EVs might end up costing more, but they might end up costing less. Also, the immediate effect of bans might actually be to create a glut of cheap, used ICE cars.
None of that implies less risk of a populist backlash, though; not for any class of 'mericans, rich or poor.
None of that implies less risk of a populist backlash, though; not for any class of 'mericans, rich or poor.