I do not think children's TV shows have recently become inappropriate. They have not gotten worse. Bugs bunny was a pretty violent kids cartoon. The characters were even shot in the face. However they do make more cartoons that are not intended for young children. There are lots of cartoons and other TV shows children watch that have warnings on them because of the violence and mature content.
Children's TV shows have not become more inappropriate and offensive. However there are a lot of shows children watch that they should not be watching including some cartoons. If a shows starts by displaying warnings then it was not meant for young children.