I don't see any evidence that you can promote genders equality meaningfully by changing the language, but I believe there is some truth to the weak form of the Sapir-Whorf Hypothesis (the theory that the particular language one speaks influences the way one thinks about reality).
It may seem odd to some in English in contexts where the gender is well established and/or obvious, but they'll get over it.
Except that's it's typically used a plural. Referring to one person as multiple is weird, awkward and clunky. Or, you're making a multi-personality joke. I thought we were at the point where poking fun at mental illness was a no-no? That's micro-aggression behavior there on your part. So sure, if you don't think about, it works. Just like saying apple instead would work if you don't think about it.
Yes, languages differ. Why anyone still uses accent marks is weird too. Oh well. A few people forcing their own ideals on the masses isn't right either. Two wrongs don't make a right.
I consider it a lot weirder that letters are pronounced differently depending on which word they are used in.
Trying to cater for people who get worked up over singular they/them is not worth the effort.