What I am about to say is going to be mostly anecdotal, with a dash of hyperbole, and a pinch of straw-man. I often see people argue against LGBT+ rights/issues with words like: "The ____ Agenda", filling the blank with homosexual and more recently transgender. Often it's followed by a rant about society falling apart and somehow that is part of the agenda. One of the most common terms in the agenda seems to be "normalization". Especially when the rant is about media that contains a minority figure. The argument appears to be summed up as: "If we normalize being gay or transgender by having them appear in [any] media then there will be more gay/transgender people! Something, something, the sky is falling!"
I am curious why it's always states as a singular agenda? LGBT people in California have different agendas than in Louisiana. There may be some (large) overlap but they are different locations with different groups of people. There is no single "leader" giving out a pamphlet with the "agenda". In many cases the people are working with others locally, not nationally/globally. If you look at the Catholic church, yes, there is a pope but there are also local churches with local priests dealing with local peoples. I can't even think of a useful analogy to an LGBT organization that functions as the global representative.
There are many things that point to this argument not being logical or thought through. The biggest one that stands out to me is the idea that having any representation will create additional LGBT people. The reason I find this strange is because the idea that you can just "turn" gay/trans seems to be at odds with the reality that you cannot "turn" straight/cis. It has been tried and there is no evidence that conversion therapy that will convert a gay person to straight or a trans person to cis. For references and sources you can read more at: http://societyforpsychotherapy.org/conversion-therapy/. I will confess I only skimmed it and I don't have a background in psychology but the language used was not so advanced that I could not follow along and it seemed like a good starting point for further reading.
Even if somehow you believed for some reason that conversion was able to work the idea still fails. There are far, far more cis hetero-normative representations than all minority representations combined. How could there be any gay or trans people to start with if every single representation was straight and cis to begin with? The most likely explanation is that there were always a group of people who did not fall in the straight and cis bucket even though the only media they ever saw was enforcing that norm.
Another common argument I see has to do with the amount of representation LGBT people are allowed to have. This is usually expressed by saying that the "LGBT Agenda" is everywhere and being forced on everything! There is now a movie, or game, or comic book that has a gay or trans character and it's destroying the world!
The first part I would like to pick out is that as a percentage I don't believe, historically or presently, that LGBT or minorities overall have been given enough representation. Some are given more than others but that wasn't always the case and the same arguments were given when they began to get more representation. Is it really inconceivable to have 1 in 10 characters in a show be gay, not even trans, just homosexual? Why would that be less fantastic than every character being perfectly straight and cis? Maybe that isn't a big deal now though. You can be gay and it's normalized. That wasn't the case always though. The same is true of trans people at this point. Why would it be a bad thing to have more diverse and accurate representations of a minority group? At this point it is a rare event that a trans figure is done right in media. Most of the time it's done by a cis person and approximated using stereotypes that are inaccurate and harmful.
Given that the majority is the one creating media the majority of the time it's not a surprise that they follow the existing majority. Since seeing straight/cis characters is the majority's opinion any representation of gay/trans characters feels like an attack or shoehorned attempt at representation. The best way to put this is summed up as: “When you’re accustomed to privilege, equality feels like oppression.” When your perspective has been represented, without exception, it feels like you are losing something when someone else gets to have any representation. It isn't a fixed pie though. Giving someone a bigger slice of the pie does not reduce the amount of pie on your plate by the same amount. Ways I can think of this are the pie got recreated in a bigger pan and everyone gets more. Maybe the pie got denser or grew along a different axis. I don't know it's a weird analogy.
The last point I want to bring up is the use of the word normalize. The word inherently biases the conversation. Why would we not want to normalize something that is not a bad thing? We normalized many empirically harmful things; smoking and drinking come to mind. There is no harm to society or individuals in being able to freely express and engage with others as themselves, whether that is staight/gay/cis/trans/etc.
Normal is relative as well. What is normal for an inner-city New Yorker is not normal for a farmer in the middle of Idaho. What is normal now was not normal 5 years ago. Normal is a moving goalpost and shouldn't be the basis for all morality. There are vague words there for a reason. One hundred years ago (1920) women were given full voting rights. Sixty years ago (1965) the civil rights movement happened that allowed African-Americans to vote (simplified). Less than five years ago (2015) the United States Supreme Court ruled on same-sex marriage. None of these things that are "normal" and (maybe) taken for granted happened because people got wiser. They happened because the minority fought for equal rights. The same arguments against their protests are used against current protesters. History has shown that we (minorities) can make progress and there is no reason to think that won't continue to be the case.