I don’t understand how Kaliya’s statements can be controversial or classed as transphobia

That’s because it’s mostly dog whistles and wedge tactics. It’s a rehashing of common transphobic talking points, but with the edges brushed off. It’s the way transphobia is portrayed to appear reasonable at first glance.

The dog whistles are easy to miss if you aren’t familiar with them, but the sheer volume of them from her shows that they were absolutely intended. This isn’t accidentally repeating something, this is an active relisting of transphobic talking points predominantly utilised by transphobic groups.

Sex isn’t a “gender orientation” it is really simple biology.

There are unspoken parts to this. What she really means here, even though she doesn’t explicitly say it, is that sex is real, and thus gender isn’t, and because of that, sex is more important than gender. It’s the way transphobic folk often phrase things so they can have a facade of acceptance, whilst still being transphobic. "I’m not questioning your gender, but you’re still male and should be denied space

Sex and gender might be distinct, but they’re related, often conflated and neither are inherently static, binary or immutable. Any attempt to draw a hard line between them, or to point at a dictionary definition is normally always said with the goal of validating exclusion, and that’s what is happening here.

Gamete size – its really simple.

This is a regular talking point used by transphobic groups. It is said precisely for the reasons I mentioned above. It’s an attempt to make a black and white, one sized fits all definition. And the reason that TERFs use it, is because to them, it’s a “gotcha” definition that allows them to exclude trans folk from spaces. And those reasons are there, but unspoken when Kaliya wrote that.

Stop confusing young autistic vulnerable people.

This is also a straight up transphobic talking point. It comes from transphobic literature that paints transgender identity as a form of social contagion, whilst also implying that autistic folk are more vulnerable to this social contagion. The specific context in which it is normally used by these transphobic groups is when talking about young trans men, by portraying them instead as vulnerable young girls.

You think it IS moral to have male-bodied people who identify as trans women playing in elite comparative sport for female-bodied people?

This is more dog whistle transphobia. The big give away here is that she can’t even give trans women the validity of their own identity. She defines trans women first as “male bodied” and secondly as “identitying as trans women”. There is a transphobic term “TIM”, that transphobes use as a slur against trans women. It means “trans identified male”. Transphobes like it, because it is a masculine name, and because it defines their identity as being male, whilst implying that the trans part is less real. The word “identified” here implies it is a phase, or a deceit.

This comment from Kaliya is using that exact concept, but just skipping the acronym.

Gender can be socially-constructed.

Sure. Parts of it can be, and are socially constructed. But what she is really saying here is that gender isn’t as real as sex.

There are only two sexes.

See my earlier comment. When you try and make things black and white, and use strict definitions, generally, the reason for doing so is to validate a push for exclusion, which is exactly what this is.

Telling male children who have feminine tights they must be female is what is happening and it is hurting boys.

Once more, portraying trans identity as social contagion.

culture has gone competely bonkers confusing sex and gender.

Explicitly transphobic. Portrays trans folk as “bonkers”.

Which is a lot of words to say, she’s a transphobe, and she is rehashing transphobic talking points, but framing them in such a way that the transphobia isn’t immediately obvious to folks who aren’t familiar with trans and gender diverse folk.