This "use LLMs as psychometric/political polling substitutes" idea seems to have jumpstarted a weird cottage industry of "synthetic" surveys. The model is pattern-matching on superficial visual cues and dressing it up as insight (I have a long beared and hence I vote for the green party).
Nate Silver put it well recently: [AI polls are fake polls][1].
An LLM inferring personality from a photo is even further down that chain of abstraction. That's not profiling, it's stereotyping with extra steps.