Well, to get some of the basics out of the way: In all scenarios people are going to come under heavy scrutiny from, well, everyone for fairly obvious reasons. Something just cosmically retconned someone's / a group of / millions of peoples' (assuming "large scale" means at least 1% of the global population) species. Not orientation, not sex, not race, not combination of the above, species. People are going to want to see if such a thing is contagious, related to SCIENCE! or MAGIC! or DIVINE!, just how in-depth the changes are, whether the original person still exists in the new being or has been usurped / replaced, etcetera. Paranoia is possible, but unlikely to occur unless either of a large scale or the majority of the small scale occurs over a small area. Er, paranoia as in mobs and whatnot. People will obviously be alarmed at the sudden presence of [x]-persons existing and having taken the place of someone they knew, but I doubt it'd stretch to full-on violence, especially if the person anthropomorphized is reasonable and doesn't do some crazy shit like try and murder the humans around them.
If this is small scale or, better yet, individual? That person (assuming they aren't in a shithole) is set for life, or if not they will be when they contact the scientific community. As much as people like to assume the default of finding alien life is "Kill it and dissect it!", real-world precedent shows the actual response tends to be "Holy fuck keep it alive as long as possible and observe it". If you're the only person who has become an anthropomorphic animal? They'll be asking you what happened, what's changed, what the different features / senses are like, acquiring blood and tissue and other genetic samples frequently (both to compare to the your old self and catalogue), making sure you're safe, making sure you're comfortable... Yes, a lot of these include having no personal time to yourself and having a lot of medical tests done on you, but notice what's missing? Vivisection, treating as animal-like property, denial of your sapience, etcetera.
Now, if you're an individual, this will likely happen until you die. You'll have people trying to clone you, see if this condition (since you rather obviously started as human) is either replicable or genetically compatible with humanity, use you as PR, publish your story, and so-on and so-on. It won't stop until you're dead or one of the above comes to fruition (ex: They start to clone copies of you, or you are revealed to be genetically compatible with something or another), in which case the focus will - while still heavily focused on you - also change towards those. If you aren't an individual, but part of a small population? This will still last a long time, but the likelihood of you eventually getting private time to yourself increases. Especially if others are found of similar anthropomorphized species as you / all anthros are found to be the same variety (A thousand anthros of a thousand different species will be nigh-on the same as a thousand cases of individual, while a thousand anthros of, say, Poodles would decrease the overall scrutiny of any one individual who didn't have something to make them stand out from other cases).
It's when a large demographic changes that things really risk going to shit. For starters, well, imagine if right now one in a hundred (just one in a hundred) people randomly turned into physical representations Neanderthals. That's it: Genetically they're still human, mentally they're still human, they just look like a neanderthal of their approximate sex and age and build. That alone would be an event that had a major impact. In this case you're having a similar (if not larger) percentage of people suddenly change their species, genetics, everything but the wetware driving them (and, arguably, perhaps even that). Some of these people physically will be unable to communicate with those around them, and others might very well go batshit insane (via either physical changes or complete mental breakdown) and start going bonkers on the people around them.
The more people who change, the more people who will be around to possibly muck up the treatment. The more alarmed people will be (as now it's not "One person in 6.7 billion" changed, nor "One person in 6.7 million changed", it's "One person in 1000" changed, or "One person in 100", or - gods forbid - possibly as far down as "One person in two"), the more likely something is going to go to shit. There is a point where things slowly start to get better (See: If 99% of the population becomes anthropomorphic and 1% remains humans, there's likely going to be a lot of contempt pointed towards the minority that didn't change. At this point it'd arguably be better for the last 1% to change too during the short term, if during the long-term the remaining humans would have the exact same benefits brought up in Individual / Small cases), but for the most part the more stress you put society under the more likely something will give.
Now, at the same time, this also means that whatever crops up after the chaos is more likely to treat those who have been changed as people (especially if, by divine fiat, all those people who are anthropomorphized animals do not win or lose the genetics lottery and are of the same approximate strength, immunities, mentality, and so-on as those who don't change) in a reasonable manner. If it essentially becomes "Racial Tension Mk.II: Species", many nations will bounce back in relatively short order. But if the new demographic is a minority? Has an exceptionally beneficial or malevolent physiology / mentality? Things can really go to shit. I mean, consider three separate scenarios:
1) 50% of the world becomes anthropomorphic animals. They are treated as human in every manner but species and appearance. Same genetic boons / banes, susceptibilities, intelligence, body capabilities, etcetera.
2) 1% of the world becomes anthropomorphic animals. These anthropomorphic animals are generally "Human, +1" to "Human, +10". Some of them are naturally Olympian athletes or geniuses (or both), and even the worst of them tend to have had their physical and / or mental capabilities improved.
3) Same as above, but now it's Humans who are the +1 to +10.
In the first scenario, you're looking at minor cosmetic differences and a tweak to what you give birth to / are reproductively viable with, that's about it. In the second, there's now a super-powered minority who are reliably superior to the majority via genetic lottery. In the third, humanity is the super-powered majority looking over a minority of frail idiots. Which of these do you think would have the most potential for a quick, relatively painless sociological acceptance?
