Not only should you not put a white light on the rear, you DO NOT need a high lumen rear light. 20 lumen is plenty for a rear tail light. I like the Planet Bike grateful red. Use two of those if you are really paranoid.
I've decided to fight back against ding dongs with their strobing headlights on the MUP. I bought a 2500 lumen strobing flashlight at Costco. Has a lens to focus the beam into a tight pattern. Going to point that right at mr disco coming the other way than politely ask them to turn there strobe off when we pass.