The problem with this argument is that you are using descriptivist reasoning ("Language is fluid", "Words are social.") to support a prescriptivist conclusion ("There's no such thing as a 'biological gender.'") If historically 'gender' and 'sex' were mostly synonymous but recently people have decided to use the words differently then that's fine, but it doesn't make it wrong for people to still use the words the old way.

> If historically 'gender' and 'sex' were mostly synonymous but recently people have decided to use the words differently then that's fine, but it doesn't make it wrong for people to still use the words the old way.

But using the phrase “biological gender” isn't using them in the old way: the way in which they were synonymous is in reference to a idea which conflated sex, gender identity, and socially ascribed gender. If one wants to refer to that meaning, there's really no reason to prefer one or the other, though either will be unclear to many modern audiences without additional explanation referencing the outmoded concept being invoked, because the concept being referred to has lost currency.

But if one is discussing the separated concepts, then one cannot honestly use “sex” for the sociological or psychological components or “gender” for the biological component and say it is the “old way”, as the old way doesn't recognize the there being separate components.

"But using the phrase “biological gender” isn't using them in the old way: the way in which they were synonymous is in reference to a idea which conflated sex, gender identity, and socially ascribed gender."

You just contradicted yourself. If the term 'gender' conflates several ideas, and adding the term 'biological' distinguishes them, then the previous poster hasn't changed the meaning of the word 'gender'. He's incorporated the new understanding but adapted the older language. Either way, the mere fact that nearly every person reading this understood his meaning shows that his expression was adequate to express his meaning.

> If the term 'gender' conflates several ideas

It doesn't. It, when used in the old sense for which sex was equivalently used, refers to one idea which does not recognize the physical, psychological, and social elements as distinct. It does not conflate different ideas, it predates the idea of a distinction; the idea of the distinction is concurrent with the terminology which incorporates it.

“Biological gender” is neither the new common usage (which labels the biological element “sex") nor the old usage (which refers to an indivisible trait.)

It can become wrong to use words the old way. Try throwing a "fag" on the fire...

Thousands of people in Britain put 'fags' in their mouth everyday. People understand your meaning through context.