I grew up in (and eventually left) a conservative Christian church, so I don't have a good idea of how aware normal people are when it comes to the fears and obsessions of that community. From stories like these I think that there's hardly any awareness at all -- which is totally fine! Those beliefs are erroneous and damaging! But two things worth understanding if you want to know why these complaints of theirs are so common (and wrong of course):

1. Evangelicals believe that if the existence of same-sex attraction is kept secret then no one would ever be gay, and

2. Evangelicals believe that sexy media leads to horniness, which leads to jerking-off, which is a sin -- whereas horrifying bloody violence does not.

It does seem that more than a few of this kind of people are quite tonedef. One example is a lot of them liking Rage Against the Machine but objecting when Tom Morello makes a political statement, as if their entire song catalog wasn't political and literally raging against everything those conservatives and/or fascists hold dear.

but it’s hard to imagine someone who thinks like that finding anything to like about Star Trek.

For those folk, my guess is they cherry pick all the flaws and celebrate them, like the:

• hyper masculinity of the Klingons
• female suppression of the Ferengi
• meritocracy of deception of the Romulans
• female enslavement of the Orions
• authoritarian control of the Founders
• the brutality to the weak of the Cardassians
• biological forced sexual intercourse of the Vulcans
• stubborn and rude arguments of the Telorites
• racism of the Andorians

They take all the flaws introduced to each race and celebrate those as evidence of an ideal. These folks don't realize that each race has a flaw in them to show their imperfection.

I like Steve Shives's video on why he thought conservatives like Star Trek.

I tend to agree, but there are two issues working agaonst Star Trek.

1. Successful media appeals to broad audiences by having something to appeal to every demographic. (E.g. Don't like politics? Stay for the lasers.)
2. Good sci-fi (arguably stories in general) gives the best representation of both sides of a conflict, and lets them compete on their merits. So it's possible to resonate with one side, then miss the critique (e.g. due to modest writing or selective hearing).

So while Star Trek tends to show progressive values winning in the end, many people can enjoy other aspects (e.g. military stories, relationships, and action) while ignoring the upshot.

I think women should be free to show their nipples as much as they want. But I'm biased, because I want to see more of their nipples.

"That nipple is too close up, I can't tell if it's pornographic or not!"