All humans fit neatly into the categories of male and female, you are either one or the other. In 99.99999% of cases, if you have a Y chromosome, you are male, although there are a tiny number of genetic mutations that can cause someone with a Y chromosome to develop to be female instead. Even in such cases, you are either male (producing male gametes) or female (producing female gametes), you cannot be both.
Humans may not fit neatly into the definitions of "feminine" and "masculine", but that is a different matter and not what was asked.
It cannot be proved that there is any such thing as a "gender identity", any more than it can be proved that there is any such thing as a soul. Therefore we should treat it as religion, which is to say, let people believe it if they want as long as they are doing no harm to others. If they try to impose their beliefs on other people or run a state on the basis of their beliefs, this should be resisted.