There are three distinct issues that are somewhat conflated here.
Issue one is having a gender neutral pronoun. This is highly important for a language to have, and "they" seems to be winning. Yay! Good!
Issue two is switching from a culture where there are two pronouns available and you should be able to tell at a glance, easily, which one to use for anyone you can see, to a culture where there are two gendered pronouns and one gender-neutral, and you may have to ask or remember to get it right. If this is rare, no big deal. If this is common, and being right is important, you've now raised the cognitive burden of everyone, while also making it harder to refer to people you don't know (if you can't always use "they"). Oof. Well. Hope it's worth it. The point is, this is not free. You now have to remember one of three options for everyone you meet. Maybe not too bad once you get used to it--at least for people whose names you know. But it's not free.
Issue three is turning pronouns into names, and insisting that people always use the right name. This is a really really hard sell, especially to people who lack either the memory or the decency to remember whether someone is named Jeremy or Jeffrey. I sympathize; 30 seconds after I hit send, I won't know whether you're Joan, Jonah, or Johan, and in a couple minutes I won't have any idea of what your name was or whether you even used a name as opposed to a handle of some sort. Because a lot of people struggle even with names (most less than me, admittedly), it seems the height of arrogance for someone to insist that everyone has to remember not only that their name is Leslee, not only that it's spelled "ee" rather than "ie" on the end, but also that they're "tey/ter". Tey's "tey/ter", I mean. The main point of pronouns is to be a compact form that can be used for convenience or when you don't know a name! Otherwise we'd just say the full thing every time.
Language is an implicit agreement between people that allows them to communicate. Change is natural, but it's important to remember that it has a purpose (communication) and is a collaboration (not a solo endeavor). As such, not everything that has been suggested regarding pronouns is equally reasonable. In particular, asking for pronoun diversity to be respected when names are already often too much seems like a losing battle, while a gender-neutral pronoun seems to make everyone's life better (except for a few curmudgeons who can't bear to update their language usage at all).