Drag sees the effort you're making and is grateful. You aren't causing offense.

Yes, "biological male" would be scientifically valid language - in part - but it would not minimise harm. Trans women is much better, you're right. Drag says it would be scientifically valid in part, because the trans women competing in the Olympics are required to no longer be entirely male. They must be on estrogen and testosterone blockers. That means regardless of what happened in the past, their body is currently performing many of the biological processes of a female, and not many of a male. In the parts of sex relevant to athletic performance, trans women are entirely non-male. Drag would say they're females, except that trans women actually tend to be weaker than cis women due to lower testosterone. All bodies, male or female, produce testosterone. With testosterone blockers, trans women are at lower testosterone levels than a cis woman.

The only thing I see them denying is that the same group of people spreading trans rights are also the ones spreading transphobia…which sounds logical to me?

We, the trans community, spread trans rights. We pressured them into putting LGBT flags on buildings. The Olympic Committee are not the government, they're a private organisation, and they weren't pressured to allow trans women by governments, they were pressured by a group of scientists employed by the IOC Medical Commission (initially, in 2003. There have been developments since then).

We have been saying the owning class is attacking us for years. It should be obvious from Trump's attacks on transgender people that billionaires hate us. And Rupert Murdoch owned media has been spreading transphobia all over the world for a lot longer than that.

If you'll permit drag to speculate as to why: Capitalism and patriarchy are very closely linked. Trans people's existence is a radical threat to the patriarchy at a basic level. If anyone can be any gender, if the "objective reality" of gender is destroyed, then gender oppression becomes nonsense. Rich white men want to preserve the social system that keeps them at the top, and trans people's existence makes it obvious to everyone that they shouldn't be.