There is nothing wrong with "they" as a singular 3rd person pronoun. If you want to complain about grammar, know grammar first. Don't overcorrect and screw up English even worse.
The problem with trying to change pronouns, aside from the preposterous motivation, is that it basically can't be done, due to barriers not at the lexical level, but syntactic level. English pronouns are a "closed class". Linguistically speaking, it's impossible to coin new pronouns. You can try, but it won't work.
Linguists classify words by how easy it is to coin new ones. There's a continuum. English verbs, for example, are very easy to create. You can verb any noun you want; I just did it. But in French for example, it's quite a bit harder, because everyone needs to know how to conjugate the new verb. Most new verbs enter French as group 1 ("manger") verbs and become conjugated thusly. It can be done, and it is done. Some new verbs even evolve irregularly somehow; it's pretty crazy. It's just harder than English, and people may prefer to rephrase or use an auxillary verb instead.
At the far end of the scale, for some word classes it's basically impossible to coin new words, due to syntactic barriers. English pronouns are an example. Another example of a closed class is Japanese verbs. Coining a new Japanese verb is basically impossible. In the last 100 years, there has been only 1 new Japanese verb (saboru). All the many thousands of borrowed verbs from other languages come into Japanese as nouns.
Interestingly, Japanese doesn't have pronouns proper, but it has a bunch of pronoun-like words which are NOT a closed class, so while it's impossible to invent a new Japanese verb, it's relatively easy to coin new Japanese "pronouns". In fact, kids these days invented calling themselves "jibun" relatively recently; it has already caught on alongside other alternatives. So in Japanese you can, at your pleasure, refer to yourself as watashi, atashi, washi, boku, ore, jibun, your actual name, uchi, or you can make up a cute pronoun for yourself just as easily as choosing a name. But this will not work in English; English is not Japanese. You can't just decide to refer to yourself as something other than "I" without breaking the bounds of the syntax of the language, and evidence shows those bounds will heal themselves and eject the innovation. You can propose new pronouns as much as you want; they won't stick. New pronouns enter or change in English only if you are looking at time scales of centuries. What the pronoun police want to do when they propose new pronouns is not only usually a stupid idea all on its own, on a lexical level, it's basically impossible on a deeper structural level. I'm not sure if they know this, or if they care. I assume they are too ignorant to even know.
