My personal take on the matter, though I claim no greater insight into this phenomenon than anyone else.
The most popular religion in the western world is Christianity, and I believe the many will see the choice be between Christian and non-Christian (in particular, atheist). Never mind the multitude of disparate groups, religions and sub-religions found in both of those camps. Most follow the religion of their upbringing, being an axiom of their worldview with little incentive to question it.
Moreover, while Christianity goes against the grain of society in some respects, there are strong rational arguments to be made in favor of these positions. Abstinence can be seen as a romantic devotion to a significant other, possibly not yet discovered. A pro-life stance seeks to protect the spark of a new human being. Even those who disagree can respect their opponents' position.
The LGBT movement in the late 20th century could be viewed as yet another example of society straying from the path of righteousness, particularly when seen as part of the promiscuity of the sexual revolution of the 1960s. There is explicit scriptural support for the condemnation of same sex attraction, both in the Old and New Testaments. Yet when society demonstrated that LGBT relationships could be as monogamous and love-affirming as heterosexual relationships, and these relationships became more public, a new challenge was made.
So Christian proponents against LGBT relationships sought additional arguments to justify their position. First it was compared to bestiality, but pointing out problems of power and consent dispense with this analogy. Then it was declared "It's a choice!" because how could God curse people with a sinful sexual attraction. Yet research seems to indicate that it's a combination of factors, including those outside our conscious control such as genetics and hormones. Then it was "They can't be good parents, it will harm the children!" but again, this line of thinking has not been born out in the research community.
Suddenly, for the first time, many Christians were confronted with a challenge to their faith which had no real answer outside scripture. Moreover, it conflicted with the core message of Christianity, love thy neighbor as thyself. How could they condemn those who, for whatever reason, were attracted to the same sex yet wanted to live a life of love and happiness? Unfortunately, the voices in the Christian community arguing for acceptance of LGBT relationships were drowned out. This muting, combined with the thrust of the new atheist movement adorned with philosophy, science and silver tongues, swayed many to not only question their childhood beliefs, but to abandon them. At least that's my take on the matter.