As a rule of thumb, some facets of the religious right like to frame any rights for a sexual minority as a form of corruption of morals or "ideology". I.E. "normalizing", "promoting".
But, of course, as society has become more liberalized, the amount of sexual violence (and other social ills) appear to have gone down. It also doesn't seem that people are less honest or other forms of morality (in fact, every generation thinks the young ones are less moral than their predecessors).
While this isn't the strongest evidence, it also appears the amount of public intoxication coincidentally decreased right around the time sodomy laws were repealed.
There also appears to be a correlation between a discriminatory law (against a particular group) passing and the number of suicide related keywords in search engines.
"promoting" or "normalizing" is also a particularly sinister form of language.
It's a stamp of approval for things which are not "promoting", therefore the only valid representation being a negative one (which can have very lethal consequences, and infringements of basic rights for minorities).
It is also a brazen attempt to silence voices of dissent (the lack of a dissenting view itself can lead to distorted views being "promoted"), because that could also be construed as "promoting". What a convenient tool.
For a more conventional example, one only needs to look at Russia (unfortunately, quite a few countries, they're just the first which comes to mind) and how they're scouring video games for instances of "promotion of homosexuality".
But, I wanted to show you how this idea has:
1) Been around for a while.
2) Gets used for all kinds of things (related to sexuality).
An infamous sex trafficking law tried to outlaw "promoting" prostitution, knowing full well that this could be construed as to cover advocacy for legalization, while pretending that it only covered running ads for specific instances of prostitution.
That interpretation got shot down in the end in the courts, although that threat was very real.