While some might consider psychology to be "lib pseudoscience" in 2013 the DSM was updated to reflect the difference between the words "sex", and "gender". Prior to 2013 they were used interchangeably as you are doing. I understand many conservatives want to live in the past, and that is certainly your right. It just might make it difficult for people to understand you if you use the words incorrectly.

As a way of thinking about this, when we were kids it was fairly common to hear the phrase "be a man". The implication of course is that "man" is a behavior. You would not say "be a male". So while the technical definitions for sex and gender may have been formalized in 2013, the actual difference has been around for generations.