I have always felt it a little jarring when I am in a party that has characters ranging from a talking bird to a centaur with nary a traditional humanoid or human in between. It really feels like a circus troupe rather than a party of adventurers. I find that to be especially the case when none (or hardly any) of the Player Characters are native to the region or are even completely unique beings. I can't specifically say that it's because I prefer a human-centric approach because I would have no problem with a majority Dwarf party, Elf party, or Gnoll party.
Does anyone else have this problem or is it just me? How can I move past it? Are there ways I can frame things in my mind to make it easier to get on with?
I’m a bit late to this thread, so forgive me if everything said below has already been said by another:
It is not just you. Mos Eisley Cantina parties are something I only allow under very specific circumstances or settings (e.g. Spelljammer), otherwise it completely shatters the narrative immersion for me.
I don’t actually move past it at all: on any pre-campaign setting guide, I explicitly list pre-approved races, their place in the setting, how average NPCs might perceive them, and how common they are. A sentence or two for each suffices. These usually include all 2014 PHB races plus a handful of others, but it can vary (in Ravenloft, I typically allow humans and nothing else). I then state that I will hear requests for other races and approve them on a case-by-case basis.
In my experience, this solves the issue. While I do get the occasional request and do occasionally approve it, I rarely actually have to deny anything; just the framing of it already leads players to finding options they want to play within the pre-listed races. If they really want to play something else, it pushes them to think about how to include it. Most players are eminently reasonable people who respect the amount of work put into the game and are happy to adjust.
EDIT: What I really meant by this is how I find it jarring when almost an entire group has no ties demographically or by any other means to the region or setting in which the campaign is held. I have found a large rise in players who come to a game with the intention to play one of the characters from their "stable" as opposed to creating a character specifically for the game they are joining.
I think what is outlined here is a different issue entirely.
Some players have characters they dream of embodying and all they want is an avenue for acting out those characters. They do not care about the setting, the narrative, or the party much at all. I find these players disruptive because in play they tend to act in fairly anti-social form (probably because they conceived of their characters in a vacuum), and they also expect a videogame/solo player coaxing to join into an adventure. These characters are typically some variation of ironic/acerbic/detached/cooler than everyone else in the mind of the player.
I think that these players are not necessarily the same people who want to play odd/furry/bizarre races. Their character could belong to a more traditional race. I do admit that there has been some correlation between odd races and “characters from the stable” in my experience, but the fundamental issues are different enough that we can avoid conflating them.
I solve this issue mostly by choosing to play with other people. Thankfully, I think this sort of player is rare.
Matt Colville had a video long ago in which he solved this issue by forcing players to roll their stats in order—thus forcing players to discover characters as they go rather than sourcing one from “the stable”. I haven’t ever used this, nor do I plan to as it punishes everyone equally, but maybe you’ll find it useful.