I actually stopped and took a couple of days to think through my answer to this, because it's not a cut and dry issue.
"The Left" is not actually a particularly useful term and here is where I have to tip my hat to Metalman. He pointed out, what 2 years ago? A specific faction within the left that seemed to the root of this.
He correctly pointed to the "progressives" as the source.
They represent a very specific mindset, rooted in Critical Race theory, Post Modernism all tied together with a fast and loose reading of Marx. They are every bit as authoritarian as anything the Religious Right can muster.
Now back to your point (which I broadly agree with). Whilst much of the left were championing for gay rights, progressives doing so weren't doing it as a rights issue, but merely a means to bolster their own platform. It was a talking point, a means to beat down hardline conservatives (as well as moderates on the left alike) and little more. The reason I am comfortable making this claim is that the moment gays got their rights, but showed themselves to be unwilling to toe the party line, they were not only thrown under the bus, but their sexuality was panned as
being misogyny's final form. So that's part of it.
The other part is something I've seen described as pathological altruism. That desire to be inclusive, even to the point where it is patently harmful, as in the case of paedophiles.
From what I can see, outside of their little bubbles, there is very little support from the wider left. However as more moderate voices have effectively been sidelined, that lack of support counts for very little. Essentially this is the Left being overrun by the loony fringe, just as the Right was a 30+ years ago when the religious extremists were invited in. It took a long time, but they gained power and left you asking "dude, where's my party?"
Even now the Right is still putting out those fires. Chances are it'll take just as long again to fully cleanse the Republican party of their influence.
The Left has been largely blindsided as most of these radicals quietly took power in Universities, whilst the moderates went out and had families and generally got on with life.
Progressivism makes up a small, but extremely powerful force on the left, far greater than their numbers would indicate. It is well connected, entrenched in academia and the media and is extremely radical.
To undo the damage it is doing in academia will likely take a couple of generations, it's influence in the media might take longer. Frankly I suspect whatever usurps the current mainstream media's audience will likely be every bit as partisan and fact free when it suits.
I've seen some right wing news outlets already making the point you did.