But none of what you've said in anyway invalidates the original question.
It's quite possibly a real issue that society may, or probably already has had to deal with, where you have trans women being put into positions where they might be speaking, or helping to legislate around issues that they have no experience of, many people might find this uncomfortable,
Just to be clear - is it acceptable to you, that a trans women, can take the position of a woman in a role, where a gender quota is being enforced? (such as government, police, NHS, etc) it seems like a perfectly valid question to me..
That's because you agree with the premise contained in the question, i.e. that democracy should be fundamentally undermined by denying people the chance to stand for election solely because of their sex. I reject that premise, so I consider any question containing it to be invalid.
Also, you're talking about a sex quota, not a gender quota. But while that distinction would usually be very important it doesn't matter in this case because the question is invalid.
You're also misrepresenting your position by pretending it's about relevant experience. That's a false statement. Your only concern is the person's sex, since you treat that as their identity (which is another premise I reject). You actually reject the idea of requiring relevant experience for a position, probably because you realise it would conflict with your belief that a person's sex is all that matters. If you supported the idea of relevant experience, you'd have to reject the idea of biological group identity entirely because you'd have to acknowledge that different people have different experiences (and are different people) even if they have a wholly or mostly irrelevant biological trait in common. You'd also have to make quotas on numerous things. Every constituency would need to have at least dozens of MPs. Every job would have to be filled by at least dozens of people.
Random examples from my own life:
Over the years, I have voted for numerous people to represent me in various political offices. Here's the radical idea you'll disagree with - none of those people were me. Every single one of them has had different experiences in life to me and is a different person to me. I didn't choose them because they had the same sex as me. I didn't choose them because they had the same gender as me. I didn't choose them because they had the same "race" as me. I didn't choose them because they had the same sexual orientation as me. I didn't even choose them because of similarities with genuine relevance, such as socioeconomic class. I judged them as
people and as politicians. I chose who to vote for on the basis of what they said and what they did, because
that's what matters.
Until recently, I was frequently seeing medical people due to non-alcoholic fatty liver disease causing worrying fibrosis in my liver. It never even occured to me to ask all of them if they had ever had the same medical problem themself because it never even occured to me that was what mattered.
Some years ago, I saw several doctors due to chronic pain in one of my testicles. It was only chance that one of the doctors I saw had the same problem. They mentioned it. I didn't ask because it never occured to me to think that was what mattered. Because it doesn't.
Many years ago, I went to a clap clinic to have a thorough check for everything. As it happens, one of the doctors examining my genitals minutely under a spotlight was a woman. The reason why there were two doctors was because one was training in that particular speciality, since the other asked if I minded if they observed. I'm fairly sure they didn't have a penis and testicles. I'm completely sure that doesn't matter. That's not relevant experience. Maybe both of them were women. I don't recall every trivial and irrelevant detail. I remember the second doctor because of the "do you mind if they observe?" question. It gave me a bit of a laugh because it seems like there's always someone to observe.