Yes! Give me a reason why not .
And here we go.
the following assessment is based on the assumption that there is a magical button that simply transforms every human into an anthropomorph with no other side effects, such as changing history.
At face value I love the idea of being my fursona, even if it were permanent, however the wanton disregard for everyone else would be a deal breaker.
Also, there are actually quite a few things of concern to consider, first and foremost would be medicine. You have over 7 billion people with now randomized DNA and potential weaknesses that healthcare providers are simply not prepared for. The compensation required to keep up with this would be unimaginable, I mean even starting an IV in a lot of instances would be impossible. The lack of capable medicine alone would likely lead to a death toll in relation to epidemics, the likes we've never seen before. I will also throw hypo/hyperthermia into this category for those that now have thick fur coats in the Middle East and those with scales and cold blood in Norway.
Another concern with the DNA would be reproduction. So we are all now anthropomorphic animals. Are we all genetically compatible or can we only reproduce with similar humanoids? Also, there are certain equine combinations that lead to sterility. Would equine anthros suffer from this? If so, that would have to be taken into account. If we
were all compatible, my next concern would be what Godawful developmental disabilities would result from certain combinations.
In a lot of cases over the world I believe there would also be panic, suicide, and massive damage to infrastructure from rioting in result of this panic.
I'm gonna stop there. Ultimately it's fun to think about, but if it were to actually happen as depicted by the OP, it would virtually be Hell on earth for some time. Fast-forwarding into the future though, natural selection would take place and those with superior genetics would be left to inherit the earth from the ruins of modern society. So I guess all in all it would end up okay for those lucky enough to survive.
So no I wouldn't press the button x.x