When it comes to trans athletes in women's sport, I think something needs to be remembered. There are numerous athletes around the world whose medal cabinets and shelves have been decimated after it was revealed that they used performance enhancing drugs and used masking agents, such as diuretics. You can't just go along and say, "My name's Mary Bloggs, I want to participate in women's sports." They'd say, "Hold on, Ms. Bloggs," and test her testosterone levels and estrogen levels. As I'm a transwoman, my estrogen levels were tested a few weeks ago, and they were found to be around 300, and my testosterone levels are just above 2. I'm not interested in playing women's sports or any sports for that matter.
The right-wing carries on about assimilation, and what they forget is, many transwomen want to assimilate into being women. Yes, a transwoman, who, before transitioning genuinely liked motor racing, might still watch it, if they weren't masking, but it's no different to a Greek person emigrating to the USA, who prefers baklava to other US sweets.