Depending on the shade of red, some colors are just going to look better than others ...and in a subjective way also.
White, black and grays of different shades pretty much work with every color. Always. However, you might not like any of them. LOL
I'm with you when it comes to white. I like white but I love just about every other color better ...for reasons all my own.
Pale yellows, off whites, different shades of brown, or grays. Olive drab can work depending on the roof's red shade.
Find a red that's as close to your roof color as possible. Either at a local paint/hardware store, or online. Then start comparing other colors and shades of those colors next to it. Pretty simple but can be tedious.
When we bought our house, it was a pale yellow with a medium red roof and light blue trim. It's a big house and any one color can be too much if not paired with others well.
We kept the house pale yellow (much like a warm white flashlight) and changed the roof to medium brown with forest green trim.
Might I suggest hot pink walls with fluorescent green trim? Huh? Yes?