Seeing Tony the Tiger on television is perfectly fine and going to Disney, you expect a hug from Donald Duck, so why are furries any different? This I am unsure of. The concepts of furry are widely accepted-- the idea of creating animal characters and having a place where they can come to life in costume form-- but for some reason, the label itself is rejected.

Some people say furs are "cringe" worthy but actually (according to dictionary.com and the sort), cringe means to shrink back or cower with fear. If this is the case, then furries should be rulers of the internet and everyone else be their royal subjects. Instead of "cringe", a better word to use would be "odd" or different".

Maybe furs are disliked because of our creativity. Furs encourage original creations like having everyone make their own fursuits. These fursuits can often look pretty bad, but these are usually the fur's first attempt at making a costume. You can see a fur's fursuit creations in the link in the description.

Maybe it's their openness in showing off art that can range from child-friendly to things even your father wouldn't want to see in his free time. Some of this art caused a controversy in Canada and America causing people to ask "is this... [wrong]?" 

No, it isn't according to the North American courts. The fursona is a representation of a person. And if two humanoids are consenting, then it's normal consensual smut. 

(I personally don't like or care for lewd furry drawings, but they can get a little weird, as can anything else like anime or adult websites that advertise OverWatch. But it is understandable how art can repel people.)

Perhaps it's the roleplay aspect of being someone else. But then again, actors on Broadway can do the same thing and have it be acceptable. Take for example the Svenn from Frozen on Broadway. The man literally wears a quadrupedal deer costume and acts like a deer.