I thought we were discussing transgender people and they are not the same as gay.  Transgender people, despite having a biological penis or vagina, "feel" they were born in the wrong body.  Even for Rachel Dolezol who pretends to be black, her race/ethnicity is not biological.  You can't "feel" you are one race when you are biologically something else.   "Gender assignment"--what an odd expression--is based on science.  A penis equals male; a vagina equals female.  How society deals with these issues depends on the prevailing social mores and the requirements or restrictions of its institutions.  We now live in a culture of moral relativism instead of moral realism, and that affects the whole society from politics to education to social issues.  I accept a person's right to do whatever to his/her body, but it is my right to not approve.   My acceptance never seems to be enough.  And then there are transgenders who change, then change back, then change again.   Google that.