LGBT+ people aren't an "agenda". Yes, it's true that the state tries to co-opt their identity to pink wash itself, but like with any sort of radical history, it tends to get co-opted.

Look into the history of events like Compton cafateria and Stonewall. LGBT+ history is just as much a part of worker history as any other group's.

On Lemmygrad?? The only argument I've seen is that imperialists claim that another country is repressing LGBTQ+ people (whether or not there's any truth to it) to manufacture consent for sanctions and the like, which is certainly true, but I'm not aware of any efforts to "push" LGBTQ+ movements domestically as a distraction from capitalism

They push it because it's an easy win. Corporations will subvert any cause that doesn't have directly to do with overthrowing capitalism. They do the same thing with environmentalism and diversity initiatives. That doesn't mean that those things are inherently bad or part of some sort of secret plot.

if you think the imperialist western countries push for ACTUAL lgbtq+ equality/rights, you're mistaken. western/nato countries are either very outwardly queerphobic (united states, united kingdom, poland, etc) or push for liberal, harmless versions of it (most of western/northern europe) that doesn't actually address social discrimination and oppression under capitalism, its just a pinkwashed facade. true queer equality is only possible through socialism, so why would the imperialist nations actually support it?