The explanation I heard was that a bumper sticker on their car outed them.

Depending on the bumper sticker, that's either absurd and a dangerous precedent -- or perfectly valid. Based on what you've described, I can only guess it is the former and not the latter.

IANAL but in California, it is certainly illegal to fire someone because they displayed a mainstream political party's bumper sticker on their car, even if it is not mainstream at the state level.