The smaller "third wave coffee" shops generally have a liberal bent to them -- largely because the movement was born in Portland and Seattle. You are much more likely to see an "ACAB" sticker, a rainbow flag, or other left-virtue device on display than anything on the other side of the spectrum.

Starbucks may be anti-union, but they have frequently taken public stances of a liberal variety (particularly around visible issues like LGBT activism, and occasionally on guns) which has left those who felt alienated as a ready market for coffee without the moralizing (or coffee with their sort of moralizing)

I often try to find a mainstream trend in the other direction to compare it to, but there are so few mainstream consumer categories dominated by the right, mostly due to demographics.