My objection with the methodology in the paper was that the authors had assembled a dataset where the distribution of gay men and women was 50% of the population, i.e. there were as many gay women as straight and as many gay men as straight in the data. This was for one of their datasets, the one were everyone had a picture. There were two more where the distribution was less even but still nothing like what it's usually estimated to be. This despite the fact that the paper itself cited a result that gay men and women are around 7% of the population.
The reason for this discrepancy was clearly to improve the results by reducing the number of false negatives which are expected when there are many more negative than positive examples in binary classification.
This from the point of view of machine learning. There were other flaws that others pointed out, e.g. the choice of metric (I don't remember what it was now, I can look it up if you like), the premising of the paper on prenatal hormone theory that is another piece of bunkum without any evidence to back it etc.
And of course there were the ethical considerations.
Sorry but I don't have the courage to reply to the rest of your comment. You write way too much.