Gender being different from sex is not a new concept, from the 2001 IOM report (predating the "gender wars"):
The committee defines sex as the classification of living things, generally as male or female according to their reproductive organs and functions assigned by the chromosomal complement, and gender as a person’s self-representation as male or female, or how that person is responded to by social institutions on the basis of the individual’s gender presen- tation. Gender is shaped by environment and experience.
Not much has changed regarding sex from 2001, we've expanded the definition of gender which is clearly much more complicated.
Who's making these arguments? A quick Google scholar was not fruitful, do you have any sources or is this a fringe minority?
> such as how your sex is listed on ID
This presupposes that sex be listed on ID rather than gender. I don't follow this in the news so I'm not sure what the arguments are but at face value using the IOM definition from 2001 ("how that person is responded to by social institutions on the basis of the individual’s gender presentation.") gender seems like the more appropriate choice for identification.