Technology

Anything else is a birth defect

Any exception disproves your rule. If you say there are only 1 and 2, and I show you 3, then the statement that only 1 and 2 exist is false, because it's only true if no other numbers ever exist. Show me a binary, I show you numbers outside that binary, it's not a binary.

Sex and gender are fundamentally the same thing

What genetic code determines things like:

1. Women wearing skirts (...while not being socially accepted for men. Except in Ireland, with Kilts, where it is, because this is cultural, not biological)
2. Men being louder and more aggressive (on average)
3. Women being better cooks (on average)
4. Socially accepted hobbies/personality traits of men/women
5. Your preference for "pink"/"blue" toys (e.g. toys usually promoted to only girls/boys, like dolls, which we have no evidence kids naturally pick along a binary line unless taught to by parents/guardians)

Oh wait, what's that? None of that is biological, but it's all traditionally gendered traits? Interesting, maybe biological characteristics and social ones aren't the same.

What about someone with Androgen Insensitivity Syndrome (AIS), where someone can have XY (usually male) chromosomes, but goes through female sexual development? Or someone with Mosaicism, who has a split of XX and XY chromosomes in their body, could have the genitalia of either group, or ambiguous genitalia, and who's split of chromosomes across their cells could be as high as 50%, or shift in one direction or the other over time. Or someone who has chromosome patterns that don't fit into XX or XY, like XXXXX. (yes, that's a real combination of chromosomes that humans can have.)

You cannot easily classify these people into sex categories, and no definition you make for sex and gender being the same thing will be capable of properly resolving which group these people fall into. You'll end up putting ambiguous people into categories that don't align with how they internally feel about themselves, you'll find ways to accidentally lump cis people into categories they don't fit in by trying to define these people into male or female categories, and that means it's impossible to make a definition that covers every single one of these people and neatly fits them into the categories you think only exist in a rigid binary, and by extension, any attempt to assign them to man/woman categories will only demonstrate how subjective the entire thing is in the first place.

Even just the fact that various traits traditionally assigned to men/women (e.g. high heels originally being worn by men) have shifted over time to being in different categories, and that different ways of self-expression, and experience, have developed over time, disproves the notion that there is this simplistic binary of human experience that cannot be un-aligned from your sex, or that certain traits are tied to sex as opposed to entirely social expectations.

And they absolutely do not have the right to start throwing abuse and words like transphobe around simply because beliefs don’t match.

Your position is categorically hostile to their existence. The definition of transphobia includes "fear or dislike of transgender and non-binary people" If you dislike what they believe, and by extension, what they are, then you are categorically transphobic. You can agree and say that you believe being transphobic is correct, but you still definitionally dislike trans people, and thus fit the definition.