What counts as "badly clashing"? I've embraced owl-folk (long before owlin came to D&D; in-setting they are burrowing owls, which actually are a thing in some desert areas) purely because a player liked owls. I worked with a player to develop his dwarf barbarian's backstory, inventing the steppe herdsmen tribes to the east, with their animal totem iconography and terrifying battle prowess that they mostly use against one another. I permitted a tiefling character, despite wanting to keep devils and demons special, and this has borne excellent fruit.
So...what would be "grossly clashing"? Because I literally cannot think of a race which would be so utterly beyond the pale that I couldn't find a way to make it work, though the player and I would need to discuss specific implementation and possible tweaks. E.g. the plasmoid people keep talking about might be an arcane experiment or an ancient relic of a lost civilization; a minotaur would likely be a native of one of the more obscure islands among the Ten Thousand Isles of the Sapphire Sea, a gith might have crash-landed on their world, etc. I find such "stranger in a strange land" stories fun and exciting, and if the player is willing to deal with the likely consequences, awesome, that's even more tools for me to frame interesting scenes with. (I should note, I find "people will be racist to you" to be utterly deplorable as far as likely consequences are concerned, so I don't do that. "Likely consequences" would be more along the lines of attracting unwanted attention, difficulties with local customs, issues if anatomical mismatch, or being hounded by someone or something.)