Maybe this will be a good place to start.
Anti-porn legislation is a decidedly right wing thing. You can see this with the laws that effectively blocked pornhub. The one I linked to includes written erotica, and non-sexual representations of lgbtqia+.
Blocking porn (or erotica in general), is a very religious right action. Associating lgbtqia+ with porn is also very much right-wing.
I don't know where youre getting the idea that religious groups are pushing left wing ideals and are therefore secretly left wing groups. Collective Shout, for example, is pretending to be a left wing group (describing themselves as "a grassroots movement against the objectification of women and sexualisation of girls in media, advertising and popular culture."), when in reality, they are tied to hard right christian groups and conservative think tanks. The opposite of what you're suggesting.
You'll often see these sort of right wing groups cover their religious based anti-porn stance by wrapping it in "Protecting the children", which will then be used as an excuse to try and prevent everything from drag shows to erotic games like visual novels. This is not "woke".
Now that isnt to say there aren't leftists with an issue here as well. There are leftists who are anti-porn. Usually though, those will be against the porn industry, and will say all porn is exploitation in some form. They won't associate gender identity or sexual identity with erotic content though, which is (usually) a good indicator of where a group or person is landing on a political spectrum. These folks are also not that common, more often you'd see the criticism limited to the porn industries where women are often taken advantage of, and the consent given is a bit more dubious.
You may also see it with leftists and specific genres of gaming, where there may be depictions of rape, especially if its shown without a narrative reason for it to exist or where its not considered wrong to have done so.
I hope you take this comment as an opportunity to understand where others are coming from, to evaluate where youre getting your information from, and maybe, just maybe, reevaluate your reactions to what others are saying.
Dungeons and Daddies (not a bdsm podcast). Especially the specials, but I relisten to the seasons. I caught it early about 4 or 5 episodes in, my daughter was just born, and I spent a lot of evenings alone cleaning so my wife could rest. I'd basically listen to all of the episodes before the next came out, just listening while doing dishes or cleaning bottles or whatever.
Its been a favorite since.