If that’s what was meant then yeah I wouldn’t mind that, but I read this as more a suggestion that we shouldn’t refer to the genders of others because doing so would leak information. I use “they” for others by default but this reads as telling me that I shouldn’t tell others I use “she” and that others shouldn’t use “she” for me to maintain the utmost of anonymity.
I think the only reason it’s controversial is that the wording of the OP is very confusing. I certainly use “they” to refer to others by default but it’s not for privacy reasons…it’s because I don’t automatically know the pronouns of strangers. I took this post as saying that we should use one pronoun for everyone to create the smallest amount of data to be collected.