If you look at the facial landmarks figure[1], it seems that the main difference between a "gay" and a "straight" man is how fat/thin their face is. Maybe gay people are on average less overweight? That's possible, but that's hardly an intrinsic characteristic. Eyebrow shape is not intrinsic either.

[1]: https://imgur.com/zs8RWIz

Social characteristics are voluntary. People who are hiding won't adopt them.

But then again, it's trivial to fool it, if the deciding fitting factor is long hair.

What is your point though? Who cares how it does it? The fact that it can tell gay from straight will have privacy implications for both. Not to mention that it is not revealed in the study how much of the feature set was based on grooming. This is pure speculation. Clearly these trigger points mean more minuses for me and a lack of any sensible discussion of the actual point of the study.