In data-centric PoliSci classes, there's oftentimes a dilemma around how to code gender. The short version is that variables in STATA are coded differently if they have a binary value (0 to 1) versus infinite options. When you mix gender into this, a dilemma arises.
The argument for making gender binary (0 to 1) is that the value for "Other / Refused" response is very low (In the Grinnell Poll from Oct. 2019, there were 17 O / R out of over 1000 respondents), and as a result has a massive confidence interval. As a result, it is considered unusable data, and thus inclusion is symbolic and unhelpful. Frankly, I think the bigger problem is that we lump "Other" and "Refused" into the same category - but if we separated them further, the confidence interval would get even larger.
The counterargument (in favor of coding with more than two options) is that not including the "Other / Refused is erasure; there are huge gaps in aid and help for transgender individuals that get so easily overlooked because of data paradigms described in the previous paragraph.
I guess this isn't so much a question as it is outlining a dilemma that I have no idea how to resolve. I pretty much always code gender with infinite possible responses myself, just because I feel like not drawing attention to the lack of usable data on "Other / Refused" isn't going to improve the situation.