Given it's possibly (likely) ostracizing and there's nothing categorically wrong about using "they" as a singular neuter pronoun, I think you're on the wrong side of this.
People should certainly stop fighting; the answer is to just roll with "they".
Douglas Hofstadter wrote a good piece of satire explaining why it's oppressive by s/man/white, etc: http://www.cs.virginia.edu/~evans/cs655/readings/purity.html
Contrary to what you say, "they" was used as the singular neuter pronoun for a long time, until a concentrated effort to force it out of use in the 1800s. Some examples from a previous thread: https://news.ycombinator.com/item?id=6824352. Some history here: https://en.wikipedia.org/wiki/Singular_they
Given it's possibly (likely) ostracizing and there's nothing categorically wrong about using "they" as a singular neuter pronoun, I think you're on the wrong side of this.
People should certainly stop fighting; the answer is to just roll with "they".