This screenshot is an example of brain-rotting stupidity that is false in everything it asserts.
Firstly, "gender" is nothing to do with chromosomes (or even biology). Gender is a socially-constructed relation between socialised bodies.
Next, since its a sociological and not a biological matter, it is not "immutable". Very little in the universe actually is "immutable" even in the material world for to be physical is to be prone to transformation. What gender is in fact is cultural.
Third, speaking now about chromosomes, its false that human beings only exist in XX (female) or XY (male) formations. XXY, XXX, XXXY, XXXXY and even possessing some cells that are XY and some cells that are XX are all possible variations. In fact, women with more than 90% XY (supposedly male) chromosomes have given birth. Judging gender by chromosomes is then just silly and ignorant.
Of course, many people may not know any of this. They may just accept what outrage merchants tell them. Educate yourself.