I think that's putting far too much credit to them having a coherent plan. It's best to take Occam's razor to these sorts of issues and look for the simplist explanations. And while the outcome is certainly the mass sterilization of many who are "gay" the reasoning behind that is most likely money

Trans surgeries and hormones regiments aren't cheap. Drug companies will certainly have a profit motivation to recommend them. And they'll have a profit motivation to lobby the government to subsidize them as that will allow them to keep prices high and reap the profits. The long term societal effects of it are largely irrelevant as they'll be seeking short term quarterly gains and retiring hopefully before the shit hits the fan. It's a problem with capitalism. You can call it crony capitalism or corruption or whatever you wish but any time profit motives are held against the well being of society and the individual then there will always be some amoral profit seeker waiting in the wings to make as much money as possible. You need only look at the drug cartels for this. Illegal yes but they don't care about the social harm they are causing so long as they can become rich.

Now this is the natural state of the world of course. The profit motivation itself is not entirely bad. We aren't going to benefit our society going after utopian communist ideals of zero property or classless societies or whatnot, but we do need to have strong laws and enforcement of those laws to protect against the excesses of the capitalist system where people will lust after riches regardless of who it harms.

The previous adoption of gay capitalism wasn't much different. Though the "rainbow Skittles" or "gay airline tickets" or whatever other marketing nonsense they came up with wasn't harmful to society in and of itself. But the motivation to market after the gays is simply driven by a desire to appeal to what is a largely affluent segment of society with high disposable income rather than any ideological motivation. The average gay couple having no children and living in "well to do" liberal cities having a large amount of disposable income to spend on various non-necessary goods. The push to legalize gay marriage comes from a similar motivation as wedding businesses certainly profit off of expanding their clientele, as well as the motivation for easier divorce laws as well can be drawn back to a similar motivation, getting married more than once means more weddings, less kids, and more money to be had by the wedding companies.

McCarthyism really did a number on the American psyche when it came to the critical thinking of these economic issues. Almost all of the social issues that the west faces today have root causes in economic issues that are allowed to take root when profiteering is allowed to continue unfettered by any restrictions of morality or common decency. That's not to say the free markets and profit motives are entirely bad things. But it's not surprising that following the massive suppression of communist ideologies through the public school system and propoganda campaigns that criticism of the increasingly corporate structures of American society was left to the outcasts and drug addicts, the hippies, and other people who simply would not be taken seriously as they were by and large idiots themselves, even when they did stumble into good ideas from time to time.

We are simply seeing natural result of what happens when unfettered capitalism needs to continue to find new and varied ways of profiteering as the "little guy" is further and further pushed out of the game by the big players and forced to beg for scraps like a unwanted dog.