'They' instead of 'he/she' is one of the things people actually use, and it's exactly dropping the gendered pronoun in favor of an existing neutral pronoun. It's strictly simpler and smaller language. My teenage kids use this construction a lot and I'm getting used to it.
1) Gender is currently a political topic. The use of gender neutral pronouns is, rightly or wrongly, associated with holding certain political beliefs. People who do not hold these beliefs are likely to reject their use on that basis.
2) Gender is a matter of personal identity. A fairly common desire for people is to be "good" at the gender they identify as. A fundamental part of that is being recognised by others as that gender. Gender neutral pronouns refuse to provide that acknowledgement.
3) They can be unfamiliar. Ultimately pronouns are something that, until recently, most people never actively thought about. Some people will reactively reject them as it puts into question their understanding of the world.
That said, I think your Orwellian concerns might reflect your personal media consumption more than the state of our changing world. People do talk about removing gendered pronouns (see: nonbinary people), and the vast majority of transgender people are attempting to assimilate into the existing man/woman gender model rather than pushing a complex system of new words and concepts. As I'm sure you're aware, both of those approaches have proven controversial and generated quite a bit of backlash, sometimes violently so.
Not everyone is cut out for a world filled with people who don't think like them. Unfortunately that's the world we live in, so we all get to figure out what to do about it.
the singular they, 'my friend', y'all, fam etc... are all wonderful substitutes for a gendered pronoun.
That sounds like a liberal feminist from ~20 years ago, trying to remove words that they think are used to oppress people. Like the people who invented Latinx.
Not to be too Orwellian, but I’ve often wondered why nobody say, talks about removing gendered pronouns altogether in formal speech instead of adding 50 new ones for instance. People seem to only talk about adding new words and concepts.