> Their facial images were obtained from their profiles on Facebook or a popular dating website

So, this seems to be doing profile picture recognition, not facial recognition. It's not like they're saying there are physical features in your face that give away your political affiliation - that is to say, putting two people's bodies under the same photographic conditions would probably not create this kind of signal.

What this is probably training on is the cues for cultural values that we self-select in our most deliberately promoted images of ourselves. If you have a carefully-chosen profile picture, it probably includes signals of what's important to you, especially if you're using it to attract people with similar values.