The networks that show these cartoons are not being forced to "censor" anything - unless Warner Brothers (or whoever the owner of the cartoons are) has specified that these cartoons be shown in their modified format. In that case, since it's their property, they can do what they want with it.
If the networks are making the modifications themselves, they are doing it with the owner's consent. There was a recent supreme court decision that addressed a similar issue (whether a third-party film distribution company could re-edit movies to take out sex, violence and obscenity), and the court ruled that companies can't change content without the owner's consent. The same principle applies here.
Most likely they are doing this because they don't want to be associated with a product that some may consider racist. They do this because of market forces: They make their money on advertising and, in the case of cable, subscriptions. They don't want their advertisers pulling the plug because of controversial material, and they don't want to lose their slot in cable franchises.
Musicians, on the other hand, load their music down with the things they do because it sells. Musicians don't have to worry nearly as much about advertisers, and the only place they are really seen on TV is in venues like MTV that just bleeps out the naughty bits (if they even do that anymore. I haven't watched MTV in years)
Basically, the government only censors the use of the seven dirty words, and there only on broadcast signals. They also do some regulation in terms of broadcasters inciting violence, but that is more directed at threats against politicians and things like that.
In short, political correctness is a function of the free market, and the natural tendency of the corporation to not alienate the consumer.
I tend to agree these works should not modified. Even a film as blatantly offensive as "Birth of a Nation" is still a benchmark in American Cinema, and should be preserved as such. And these cartoons are nowhere near as intentionally racist as that film. They are, as was pointed out above, more a product of their time than anything else. But that is a very nuanced argument, and outside of academic circles, you are going to find very little popular support for it.
The good news is that I believe you can still get these cartoons in their original state. I know you could back in the laser disc days, because we sold them at an educational film distribution company that I used to work for. Also, they show up in the artsy movie theatres quite frequently.