I think you're severely overstating the effect of LGBT people on this matter - western countries struggle with demographics, but it's not because more gay people are able to live their lives without being forced into straight relationships.
https://link.springer.com/chapter/10.1057/9780230554993_4 https://bmcwomenshealth.biomedcentral.com/articles/10.1186/s...
(Also, American elites don't really see themselves as struggling demographically.)
Personally, I think they also like being able to blackmail powerful LGBT within their countries/satellites. Historically, when their targets realized that America's fairly tolerant towards foreigners, leftover women, <i>and</i> LGBT people, their targets tended to defect.
Not my views, what I see as the reasons traditional conservatives want to keep LGBT acceptance to a minimum.
LGBTQ rights are a sub-set of human rights, in which individuals have self-autonomy/integrity. This may be antithetical to more traditionally collectivist cultures.
An independent judiciary and due process also has a noted history in the West as compared to how things were run in (say) Imperial China:
* https://www.goodreads.com/book/show/3624887-the-medieval-ori...
Assuming that queer people will somehow take over the world and cause an unsustainable birth rate sounds a bit like the right-wing "gay agenda" conspiracy theory. Not to mention that people born with a vagina can have a male gender identity and still get pregnant, and some trans women can get others pregnant. Sex != gender. Also because gender identity isn't just a lifestyle choice, it's not like all the straight people will somehow get converted.
The Party forced the population to HAVE fewer children in 1980. They did this primarily to jump start their economic modernization plans. Moreover, they figured everyone would start having kids at replacement rates second they lifted the rules. If that happened, they'd be able to consolidate their economic gains.
Economic modernization worked. The kids part...not so much. In fact, there's reason to believe (e.g., maternity store receipts) that their birth rates will look like Japan's or Korea's.
To put it another way, not only are people having fewer kids, they're having far fewer kids than Westerners with equivalent per capital wealth/income are. If that happens, China may not be able to consolidate their economic or international political gains. THAT is what Chinese elites are really worried about.
I, personally, am interested in the elephants in the room. For starters, my lesbian friends and I really wonder if the Chinese censorship machine are responsible for erasing lesbians from Western media spaces -- and especially LGBT spaces. Everyone hears plenty about bi and trans women, but lesbians? Nope. But we're still here.
While I'm not the only one who's noticed this erasure, I think I may be the only one who's also noticed how China's quietly been rolling out aspects of its online censorship system in the West over the past ten years -- and how it's REALLY intensified over the past five (i.e., doxxing, career ruining for anyone with political opinions threatening to the current leaders, sex pic leaks against political opponents, etc.). Guess too many of the Chinese kids studying abroad decided to stay abroad, so it's time to make the English internet feel exactly the Chinese one. Sadly, now the air sucks just as much here. Thanks guys.
More substantively, I find it interesting that absolutely no one will discuss how women in fully economically developed Confucian societies have FAR fewer children than equally economically developed non-Confucian societies (e.g., South Korea and Japan vs. Italy and France).
Authoritarians instinctively cling to the old roles/family and even if are not able to fully stop changes (US is amazing at exporting ideology) they try to and battle against LGBT is part of that fight.
I do not think you can directly connect authoritarian and being anti LGBQ outside of modern context - Xi, Putin or Orban views on lgbt were mainstream in US only 20-30 years ago.