I gravely doubt that anyone has that expression permanently stuck on their face. The image you linked to was obviously created in order to show "SJWs" in a bad light, and I can't imagine that anyone wanting to do that would use typical photos rather than particularly bad-looking photos for that purpose.

(The SJWiest people I know do not generally wear that sort of expression.)

I'm sure you're right that treating impurity and disgustingness as moral is not confined to the political right.

I suspect that the things treated as disgustingly wrong in "social justice" circles tend not to be ones that arouse feelings of disgust, as such, in most people, whereas things treated as disgustingly wrong among traditionalist social conservatives are often more widely felt to be disgusting. To put it differently: I suspect that "moral disgust" takes different forms on the left and on the right: on the left it's usually moral disapproval that has engendered disgust, and on the right it's usually disgust that has engendered moral disapproval.