I have some friends who are really into Constructed Languages and it's a really interesting domain within which to explore questions about which distinctions are worth marking in basic grammar. Romance languages famously like to gender everything (even inanimate objects), obsessively mark singular/plural, and have a basic status marker via the T/V distinction. Homeric Greek marked the distinction between two people and 3 or more people. Japanese, Chinese, and Austroasian languages don't really care about gender and number but care quite a lot about status markers (especially in Chinese and Japanese). And Austronesian languages really care about the inclusive vs exclusive "we" (basically the difference between "we" meaning "me and my friend here" and "we" meaning "everyone in this conversation").
My general sense is that there's no neutral way to decide what's worth marking and what's not. "I met a man today" vs "I met a person today" vs "I met someone of higher social status today" vs "I met <instance of humanity> today" all have different significance and I like the fact that different languages forefront different things. But I think any political program that begins by saying "we need to convince 300 million people to adopt a different grammar" is hilariously doomed from the outset.
Your comment raises the question about what kinds of changes people would be willing to accept.
New grammatical rules are a pretty good entry for "would not accept," though it's not a perfect rule and there are a few exceptions. Singular "they" for unknown pronouns has caught on, it remains to be seen if singular "they" as a preferred pronoun will catch on. Whereas "it" or "zhe" or "xhe" will probably never catch on.
On the other hand, people accept neologisms and new phrases all the time. Off the (culture war) top of my head, "cancel culture," "snowflake," "safe space," "own the libs," "thot," and "galaxy brain" have all caught on, even though nobody can really agree on what any of these terms mean. People willingly accept phrases like "social media" and "email," there's some fussing about the names at the edges but most people learn the new word and move on, because it ends up being pretty useful.
Usefulness might have something to do with it, because "useless" words have a much harder time catching on. Our ideas of "useless" do tend to vary by personal taste. But not many people are going to care about the fight over "trans woman" vs. "transwoman," for example. And whether you accept that calling something "gay" is a sin or not probably correlates with your attitude about how much of a thick skin one should have around "mean words," i.e., how effective it really is to police these kinds of things.
I'd be interested to hear other takes, but my intuition is that people accept changes on a cost-benefit basis, the harder the neologism the more worthwhile it has to be to accept.
Since you brought up constructed grammars and linguistics, I'm reminded of the concept of the Idiolect. An idiolect is a person's unique way of speaking, the language particular to one individual. We all internalize grammar and vocabulary slightly differently, there are some formal rules or standards but they're not totally enumerable. (If they were, we could program robots to follow them all.) In one sense, we're all really speaking different Englishes. It's only because our idiolects overlap so closely that we're capable of understanding each other. If we mapped our idiolects as Venn Diagrams, we'd be mostly overlapping, though it's easily possible for me to speak some other English that wouldn't overlap as much -- innit?
I reference this because I've always been struck by a slight ambiguity in the idea of the idiolect. It strikes me that an idiolect could refer to two things. It could refer to someone's unique speech within a language -- the particular way I speak English that's different from everyone else. Or it could refer to someone's unique speech across all languages -- the particular way I think sometimes in English and sometimes in Chinese. Thought of another way, is the unique way I use language bounded and shaped by other people? Do I have an English idiolect and a Chinese idiolect, each roughly bounded by our shared common understandings of English and Chinese? Or do I have my own, personal, private space where English and Chinese mingle and neither English nor Chinese norms quite govern how I think?
I think this is important because the question of how people relate to their languages is a key question in how politics intersects with language. The classic example is always 1984, where language is tightly controlled by the government. "Newspeak." Would the government of Airstrip One want to ban foreign languages? Or just foreign vocabularies? Because there is some definite ineffable quality in the grammar of a language, none of us can ever quite express it, but we all know intuitively that "Latino" is normal and "Latinx" is weird -- even when we mostly speak slightly different idiolects.