3rd/non-gender people are medically and scientifically separate - this is the consensus,
You are seriously confused. Male and female are sexes. There are no third sex, and nobody can change sex. People who identify as transgender are not additional sexes, although those who have dysphoria are unhappy with their sex or sexual characteristics.
If 'gender' is separate from sex and consists of social roles and expectations assigned on the basis of sex, then it is not a medical or scientific concept but a social one. The decision to put people who don't identify with the social expectations associated with their sex into another gender category is not a medical or scientific decision, but an ideological or philosophical one. Just as it would not be a medical or scientific decision if society decided that a male person who is attracted to males can't be a man because society expects men to be attracted to females, therefore they have to be removed and put into a separate category (which would of course be considered regressive).
Perhaps you have read some ideologically motivated rubbish in journals about sex not being binary and mistakenly think this is based on some type of scientific discovery.
they are not mentally ill, they are not somehow sick,
Irrelevant. If society decided that gay males have to be removed from the category 'man' and put into a third gender category, and a psychiatrist subsequently examined these males and concluded they are not mentally ill, it wouldn't demonstrate that they aren't men. That's because the only reason they would not be considered men is based on the social definition of 'man', which is not a medical decision.
BTW, I'm pretty sure that there are many transwomen who would take grave exception to your describing them as being in a different category to adult human females, so assuming that you want to jump on the activist bandwagon, you haven't even got that right. Most transwomen do not want third spaces, although some do.
they are people who do not belong to either female/male category.
No, everyone is either male or female, even virtually everyone with a so-called 'intersex' condition (there might be a quibble about a few extremely rare cases with both types of gonadal tissue, but that has nothing to do with transgender identity). You can change some sexual characteristics, but trans activism says you don't have to do this to count as trans. There is no evidence that a male person who is gender non-conforming or doesn't feel male is somehow different from other biological males in regard to the small number of situations where we have sex segregation, even if it were possible to verify their feelings.
So you are for collective punishment based on belonging to a group? And for limiting rights that are in a modern society attributed to that group with presumption of guilt? And yet giving a pass to the foxes in my analogy?
Don't be ridiculous. Nobody is advocating punishing anybody. Modern trans activism is seeking the replacement of biological sex with gender identity. This is based on postmodern theories that are incompatible with scientific skepticism (that's why they consider it acceptable to decide on an ideologically desirable conclusion first, then construct the 'science' to support the conclusion - since science is just a narrative constructed to serve the oppressor).
Human rights is not about bathroom stalls - if you feel that that is the problem there are several totally viable solutions to that (unisex bathrooms etc etc..)
Pro-sports - not really a issue, private "companies" run these with their own guidelines and divisions and series. I don't see much complaints about any other genetic advantages in sport though I think I laughed at some "white only" - basketball league attempt at some point but not sure if it ever happened.
If you think males do not have advantages in sports over females, then you are advocating the abolition of sex-segregation in sport.
