system
A chat on subreddit /r/PoliticalCompassMemes
human
I realized that the main thought process behind LGBTQ+ stuff and people having "their own truths" is based on whether or not there is objective reality/morality. 

L: "Define a man"  
R: "A human male with XY sex chromosomes"  
L: "What makes him a male, and what makes the chromosomes XY?"  
R: "... he is biologically male. Every cell in his body has those chromosomes"  
L: "What makes those chromosomes XY though? What defines them? Langauge?"  
R: "The chromosomes have structural differences"  
L: "who says that structural microscopic differences have to impact our language? what if I say that a man is whoever thinks he is a man, and that's what makes him a man?"  
R: "Well that's not supported by the majority"  
L: "Is it not? So in a town, what everyone agrees with is truth? I believe each person can assign reality their own truth, as that is all reality is to them."  


I'm sure this is a really bad explanation of metaphysics, but I hope you get my point. Reality itself is based on objective morality. Without religion, there is no God to say "this IS man, this IS woman"- anyone can just claim that what THEIR eyes see or THEIR minds believe is THEIR own truth. And that's all there is to it.   


TLDR: LGBTQ holds that identity is self-created, as all that matters to an individual at the end of the day is reality as they perceive it, not how others agree it "is"
gpt
You can still think they shouldn't exist without objective morality or truth, it might even be easier.

Generally most people pushing for it believe in objective truth, and base their arguments on that. Only a small subset of them makes the argument you're presenting.