Some of the secular media is very conservative regarding LGBTQ issues, but much of it is either neutral or positive on those topics. There is no general "media" one can talk about in this country, especially on specific issues. The media, also, in large part, is neutral on religious issues, out of concern for its audience, which includes people from all religious and non-religious positions.
It is a mistake to lump all media into one group - a grievous mistake. It implies that most media is similar to Fox News, which has a clear and obvious bias on both LGBTQ and religious issues. That is not the case, on those issues, at least.
Guess which television news media has the highest numbers of viewers? It is ABC, CBS and NBC broadcast news, by a very, very large margin. You will not find open bias for anti-LGBTQ issues nor for right-wing Christianity on any of those three. They simply do not have those biases, generally, but take a neutral to positive view of LGBTQ issues and mainstream religion.
The author is mistaken, if he or she lumps all media together. That is simply not correct.