It seems fairly clear that neither of you are happy with the definitions that other people in the thread use for the terms male/female/ethnicity/race. In order for the discussion to actually be a discussion you have to give your definitions of the terms.
From the sounds of it you think of the terms as all abstract with no actual possible set of criteria. Yet I cant see the use for the words at all if they have no actual definition, and rather than arguing that we should abolish the words from our vocabulary as they can no longer have a definition you seem to be arguing that we continue to use them, but with no actual definition.
Some of the words have meaning some don't.
Race, as it refers to people, has has no useful definition and should be purged from our language.
Ethnicity has a specific definition, and when the word is used with that meaning is a useful word. Ethnicity is about belonging to a social group and has little or nothing to do with biology. Ethnicity is not exclusionary. A person can belong to dozens of different ethnic groups. Unfortunately, in common parlance, people more often than not use it as a synonym of race.
Male/Female is useful, but the definition is not quite what people think. Male/Female is not a dichotomy, they are the extreme ends of the spectrum of sexual morphology. Change the morphology, change the sex. I would also mention that currently our culture is struggling with the terminology to describe various points on the sexual morphological spectrum. There are lots of competing words and definitions. There is still work to be done before we settle on a set of words and syntax to use.
Gender is even more complex than sex, gender can be more thought of as sexual ethnicity. It is the sexual group you identify with and it is not a linear spectrum between male and female any more than cultural ethnicity is a spectrum between white and black. Like sexual morphology above, we are still working out the language for this, and how it interacts with sexuality.
I believe that the problem most people have with these things is that they want them to be simple and they just are not. Most people want to be able to point at everyone else and know what group each person fits into, all the while being must too deep and complex themselves to fit neatly into any such box.