Fur grafts, tail plants, facial surgery, all extreme solutions to what seems like a trivial question: Can I be more like an animal in form and function? Obviously some humans are growing desperate to emulate other, more physically capable species in the animal kingdom.
At this point, medical science is making leaps and bounds in the understanding of physiology, but is still limited in the ways it can be changed to treat ailments. Generally there are only two means to this effect: drugs and surgery. Drugs aren't as well understood as one would hope and have often proven to have an equal and opposite reaction, and surgery is limited in scope, difficult, expensive, and poses myriad risks.
For the purpose of treating disease and injury, medical science is far more capable than it was a century ago. However, it would be foolish to use the limited medicine of today for anything else. Those who modify their bodies into the image of animals have been left to the ingenuity of not doctors but artists. The practice of such extreme modification will require techniques that will cater to both.
The future likely holds such devices as those similar to the replicators in the Star Trek series of television and cinematic productions. Using cold fusion technology the properties of anything, including living forms, can be altered to the precise specifications of the user. This heralds in a time when one can change "species" as easily as one would change clothes. And it's closer than you think.
Form versus function is an important question in making these determinations. Some, and not even critics, have raised the fact that a real life furry would not look as flattering as depicted in paper and digital media. Regardless, the capability to emulate the forms and functions of animals raises interesting possibilities.
Some might equate becoming an anthro furry to wearing a fursuit, but it is much more than that. Being able to modify the human form into anything does not simply mean one can be a furry, but one can look to nature to enhance human engineering. Any combination of features for form and function can be utilized, making it possible to live comfortably not wearing a fursuit but being one.
For instance, being the size of a human, covered in luxurious fur (and hopefully wearing some clothing) and unable to sweat may be quite hot in the literal sense, but having large ears like a fennec fox that radiate heat could help offset this, not to mention funnel sound far better than human ears.
Whether such a thing is ethical now is a moot question. I am confident that the development of such technology will have an effect on society much more profound than the ability to look like an animal. This type of socialogical singularity is impossible to predict, but one thing that one can always predict is thus: make it possible and it will happen.