What are some of the changes you would expect in a furry reality?
Everyday things would be different. You have to account for tails everywhere. Bandaids wouldn't work with fur. Would shirts be worn, or would natural fur coats be all that is there? Food workers would have full body nets. Claw tips come out of a different area and would make some tasks that use fingertips difficult (typing)...
I think Band-Aids would still be a thing; we would just have to shave the area before applying them.
Not sure if clothing would be for more than just fashion. I suppose people could still have the same sensibilities about nudeness, even if most species have built in genital coverings.
Make-up might not exist.
Depending on how much variety was in hands, there may be an even larger variety of hand-tool styles.
I would suspect that instead of your traditional bandaid with a sticky side instead a version where you tie it on would become more popular as you wouldn't have to worry about shaving the area first. I think there would also be more markets that advertise to specific species. As for hygiene I would imagine that grooming products would be very popular as nobody wants to deal with a mouthful of fur or coughing up fur balls. I imagine that touch screens wouldn't really be all that popular for the reasons that you mentioned and that buttons would be used as pressure sensitive screens could be damaged more easily by claws. I do believe that makeup would still exist, but it would likely be in the form of fur dyes or powder that can be easily washed out, especially since the majority of mammals dont sweat so it smearing would be a lesser concern.
Species would be more geographically separated due to temperature tolerances throughout the year as they would be more likely to live in areas more suitable for them. On a similar aspect, I think they would wear less overall clothing due to fur making it easy to get too hot. Vehicles would likely have taller roofs to account for ears. If the size range on species is large enough I would also imagine that there would be doors within doors or multiple doors of different sizes to allow for smaller species and larger species to be accounted for without making too many modifications to accommodate them.
The whole field of ergonomics would be a lot more interesting. The diversity of body shapes means you don't just have to account for larger bands of possible dimensions, you may need to account for entirely different anatomy. These would follow through clothing, furniture, construction, accessibility laws, etc. There wouldn't be just one new shape that's different to ours, there'd be dozens to account for.
Touching on just construction for a moment, there's a concept in at least some countries of what can be advertised as livable space, the most clear example being minimum ceiling heights. With a broader array of body shapes, lawmakers have to make a decision between allowing residential buildings to be advertised with a limited category of occupancy (necessitating the creation of several classes of living space with different requirements) or requiring every residential space to be built to at least physically fit every potential resident, no matter who it's advertised to. Commercial and industrial spaces obviously would all have to fall into that latter category anyway.
Stairs provide a more difficult problem, because you can't just size them to the largest possible resident, nor the smallest. You could create steps with multiple sizes side-by-side, but that requires more space; I suspect ramps would be far more common than they are in our world as a "one-size-fits-all" solution. Can you imagine a world where everyone expects a ramp up to the second floor of their home before they expect stairs?
A struggle against prejudice and xenophobia on a much greater level than humans have with only one species, debates on whether it's ethical for a couple to produce an anthro mule or other infertile hybrid, any modern mixed-species regions would need a very complex design to accommodate everyone's different biological needs even if all the anthros are nearly the same size, the study of evolution would be a lot of fun because a diverse anthro world requires many distinct intelligent species to emerge very close in time to one another, endless other worldbuilding opportunities
Opposable thumbs are kinda important to everything. Climbing, throwing, manipulating. Basically the entire industrial world and all products. I think of my days working at an asphalt plant. No machinery is possible as it is now, cars, driving, maintenance of anything; it all requires thumbs. The extra step of some kind of prosthetic manipulator would make everything prohibitively expensive impractical IMO. It would be a world of cave life without tools and fire.
Assuming we're talking animal anatomy (and not 'hands' on species that normally have paws), all of the jobs and societal roles that require fine manipulation would be limited to a fairly small number of species. Monkeys would likely be very sought after for most of those positions. Rodents would likely be pretty high on the list, too. On the other side of things, canines and felines - despite their popularity - would have the hardest time with things. Never mind things like marine mammals and birds.
Do otters count with marine mammals? Birds are very good at manipulation and some can create some tools. In your description I think that world would have some pretty serious segregation issues.
I am not into furry stuff (saw this in the New/All feed). However, I am very into AI roleplaying, hard science fiction, and this overall idea of how things might be different under some arbitrary ruleset. IMO, the less that happens "off screen" the more stuff becomes interesting to a wider audience.
I have trouble picturing the fundamentals like machining, welding, foundry work, all the way to maintenance. Like picture yourself changing a flat on a car and trying to replace the wheel with the spare. Ladders in particular would be out. Around the home, it would likely be easier to clean something like a grill you might find in a restaurant's kitchen than it is to manipulate pots and pans. A joystick might be easier than a steering wheel. Elastic closures on clothing would likely replace buttons, zippers, or lace ups. Those are just a few I can think of off hand.