Only one of many reasons of course, but when I was living in a conservative part of the US, I ran into a lot of people whose perception of equality/inequality was very sensitive to "the rules are changing" as opposed to how people are affected by those rules. Since they or people they know have made a lot of sacrifices to conform to societal expectations, it strikes them as deeply unfair when such expectations are not enforced on others. It's the sort kind of reaction you might have when playing a game, and midway through your opponent suddenly invokes a house rule they never told you about. Not only would you be upset about the surprise, but you might worry about getting caught off-guard again in the future or be suspicious that the house rule was made up on the spot to disadvantage you. But life isn't just a game, and we don't get any chances to play again, so, understandably, these people take actual societal changes much more seriously. What they don't seem to focus on as much is whether the original societal expectations are beneficial or not—they may well be aware that society treats some groups badly, but see that as either an ineradicable problem or a necessary evil to avoid pulling the rug out mid-game. As someone with a pretty consequentialist outlook, that meant that these people and I were talking past each other a lot, not only on LGBTQA+ acceptance and rights, but on any issue where society is changing.

Interestingly, for those who have being Christian as an important part of their identity, Jesus actually preaches against this kind of thinking in the parable of the laborers in the vineyard at the start of Matthew 20. I also happen to be Christian (though the kind that wonders how anyone could see the gospels as anything but pro-LGBTQA+), and I have had mild success bringing up this story and just finding some common ground on what "fair" means before getting into more specific topics.