Trans people say they identify as the opposite sex

You can't "identify" as something biologically different than you are any more than it would make sense to identify as a horse or a plant. Humans cannot change sex.

Nonbinary people say they identify as neither boy/man nor girl/woman

This is all based on stereotypes and they imply the rest of us all do identify with those stereotypes which is insulting.

one day they feel like a man and the other they feel like a woman.

What is feeling like a man or a woman? One day they feel like playing with dolls or going clothes shopping and the next they want to watch football and work on their truck? Do you realize how sexist and ridiculous this all sounds?

People aren't "cisgender" we (mostly) don't identify with gender roles but have them imposed on us as children.

While the others identify as something other than the sex that was assigned to them at birth.

"Assigned sex at birth" is an intersex-term which does not apply to none intersex people. It is easily observed.

What is born in the "wrong body"? How would you even know? You have nothing to compare it to as far as actually knowing what it would feel like? The whole thing is so bizarre and pseudo-religious like you just "know" you're "in the wrong body" somehow. I really don't understand how non-mentally ill people believe this.

What does "invalidating someone's gender identity" even mean? If it's something that really exists then they should feel it very strongly and not be threatened when other people don't believe in it. But I don't see why I have to pretend to believe they are the "gender" they say they are when I am anti-gender as a whole. It is like saying I have to pray with someone and really pretend to believe their religion is true.

Now you're actually saying that other animals have gender identities? No. Other animals instinctively know what sex they are and how to mate. Animals don't have gender roles to identify with. Gender roles are a human construction.