This is a non-Christian perspective, but I think there's something to contribute.
People have been shifting their time away from in-person social organizations like churches for decades (see Robert Putnam's Bowling Alone). This shift has coincided with a steady increase in the amount of "screen time" we expose ourselves to, as the screens have improved and become better at meeting our needs. Thus the things people used to do in church are now being done on a smartphone or computer.
- Entertainment has shifted from church socials to Netflix and YouTube.
- Appreciation of music and art is now done through Pandora, Flickr, etc. rather than choir, or church art.
- Dating and sexual opportunities have shifted from arrangements made at church to dating apps.
- Job networking has shifted from social networks at church to Indeed.com and LinkedIn.
- The social support net has shifted from church "charity" to GoFundMe.
- Social communication and keeping up with friends shifted from church to Facebook, Instagram, Snap, WeChat, and text messaging.
- Comforting senses of meaning, belonging, and certainty have shifted from religious dogma to often-politicized social media tribes on Reddit, Twitter, Telegraph, etc.
So thanks to advances in technology that started with television, the average person has a lot more ways to get their needs met. Also, this new lifestyle is much cheaper than being a church member, both in terms of money and in terms of intangibles such as travel time, having to deal with difficult people, and church-imposed rules one has to conform to.
Another way of saying it is that the hours per day people now spend staring into screens came from somewhere, and it wasn't work, sleep, or personal hygiene - it came out of their time spent in social organizations. This is why church membership has declined from 70% in 1999 to 46% today, and is still falling hard.
Of course, if you are running a church and your donor / volunteer base drops 34% that doesn't make the organization any cheaper to run. Each remaining church member must pay more, volunteer more, and spend more time doing less-rewarding activities like recruiting to keep the infrastructure afloat. They will have to submit to stricter behavioral rules and norms to maintain internal cohesion amid these rising costs.
Churches that stick to their old formulas are dying, leaving behind the churches that have moved to the fringe as the only ones still growing. The result is churches that are politicized and almost cult-like in their narratives of persecution and imminent end times. If even a tiny sliver of the population can be persuaded to believe these things, they will commit more of their time and resources to their fringe church, and it doesn't matter whether that church can ever appeal to a wider base or if they are running off their moderates. They are at least surviving in a world where the moderates are investing more in screen time.
This is where the fixation on sexual deviancy comes from. Hateful attitudes toward sexual minorities and nonconformists provide a rallying cry to keep the ingroup together despite the rising costs of membership and falling attendance. Again, this might only appeal to a small minority of religious folks, and it may run off the moderates, but the organization's agenda is set by the fringe who are willing to devote more of their time and money to the group.
The whole reason religion got into arranging and regulating people's mating habits is because people needed an institutional solution to the problems of infidelity, males fighting over females, people's anxieties about never finding someone to mate with, and the problem of heterosexual fathers not supporting their offspring. Left unabated, these challenges would shake the foundations of the tribe or civilization. Heterosexual monogamy enforced by religious codes and public "wedding" ceremonies - where the church gives two people permission to fuck - were the solutions. This became a key product the church was selling. You had to conform to the terms of the church's "marriage" product, but the church would with near-absolute certainty get you laid. The church's "marriage" product was better than any other option women had to pursue their reproductive goals with male commitment, so that's where the women went. The males of course, had to follow. To this day most churches are actually run on a day to day basis by a group of women.
But this whole set of problems seems outdated in an era of birth control, condoms, and dating app culture. Religious opposition to birth control, abortion, divorce, and sex outside of marriage can be seen as an attempt to preserve the religious monopoly on access to sex. To the extent "Adam and Steve" don't have to worry about partner's commitment to the baby they will never produce from their sexual encounters, their "gay lifestyle" represents a competitive product in the minds of religious conservatives. It is perceived as a threat to churches the same way Uber is perceived as a threat to taxi companies.
Of course, this sounds like nonsense to anyone who is strictly hetero, but as we now know sexuality is a spectrum, and there are probably many married people in churches with suppressed same-sex attractions or gender fluidity. To them at least, the "LGBTQ lifestyle" might seem like a compelling alternative to their church-arranged marriage. They are personally tempted, and so they see sexual preference as a choice anyone can make (it is not). They also see their temptations as a threat to their marriages and church community.
Any lowering of the disadvantages for women is thought to reduce their dependency on the church's "marriage" product. Birth control, abortion, and divorce are seen as wrong because they reduce the costs of not being traditionally married. Without the disincentive of single motherhood, it is thought there's less of a reason for attractive females to participate in the church's mate-arrangement program. And of course without attractive females, the males go too. Resistance to reproductive technology is perceived by the churches as a matter of survival.
Dating apps and casual safe sex, backed by the option to abort in the event of a contraceptive failure (up to 1 in 20 odds), arguably offer women better opportunities than marrying someone from the small pool of men in their church, and waking up to his farts and other shortcomings every morning thereafter. If the women quit church, the men quit too, and the church collapses. The only way to head off this outcome is to effectively ban the alternatives. Also see: Indonesian conservatives just outlawed sex outside of marriage.