I'm not a linguist or language historian, but I've read a bit about evolution of the English language, so take this with a grain of salt.

Language generally changes organically, I think it's pretty rare that intentional campaigns have the desired results. Euphemisms arise and change due to general societal attitudes. For instance, the advent of the civil rights movement led to derogatory terms for races and ethnicities becoming mostly taboo. "Mailman" became "letter carrier" as more women entered the occupation and American society became less sexist.

But there were no organizations waging public campaigns to stamp out the N-word and sexist language, for instance. In fact, I think such campaigns are likely to backfire, as people tend to resist being told what to do. Negative reactions from peers are likely to be much more effective. Some countries have organizations dedicated to maintenance of the language (like [L'Academie Francaise][1]); they exercise some control, but you can't stop people from talking the way they want to talk.

These particular replacement idioms seem pretty ridiculous. The originals are clear metaphors that make sense, the replacements were chosen simply because they sound similar. That's not to say they can't catch on, as many euphemisms are also sound-alikes (e.g. "Crikey" for "Christ").

PETA in particular has a history of going to extremes. For instance, while the organization probably officially denigrated such acts, people aligned with them have been known to throw blood on people wearing animal fur. And they've put up billboards that many have found offensive. They're a very polarizing organization, and this is likely to bias many people against this latest campaign.

This PETA campaign reminds me of when a faction in the US government attempted to rebrand French fries as [Freedom fries][2] because France opposed our invasion of Iraq after 9/11. The change was made in the menus of the Congressional cafeterias, but it never caught on more widely, and 2/3 of respondents in a poll at the time thought it was silly. The cafeterias changed their menus back 3 years later. 

Perhaps if they could have convinced McDonalds to go along, it might have been more successful. But there's no analogous organization PETA could turn to to try to get their phrases popularized, so it's likely even more doomed than that was. It will probably be the butt of a joke on Weekend Update this week (as the Freedom fries attempt was 15 years ago), and then promptly forgotten.


  [1]: http://www.academie-francaise.fr/
  [2]: https://en.wikipedia.org/wiki/Freedom_fries