I read a little about them and I can't say I find their strategies very good.
Navagon: Precisely. PETA mass slaughter domestic pets because of their warped ideals that every animal should be free from 'slavery'. Naturally pets don't fit into their completely batshit insane views so they have to go.
I think that is a nice ideal with some exceptions like dogs, cats and probably some other animals too. Dogs seem to be naturally inclined to dominate or be dominated. In a good family they are a part of the family, I think that is a good thing.
If some people think that all animals yearn to be free they are blinded by their ideology. However if you compare that blind spot to the common (self-chosen) blindness to the suffering we subject animals too I don't have a problem seeing who is the most blind.
I would surely support a ban against keeping birds in cages. There are many other animals that ideally should not be kept as pets but you have to start somewhere and the worst should be targeted first, like the industrial pig and chicken farming industries.
About the slaughtering of pets you mention, to what are you reffering? The wikipedia article said this:
"PETA runs several programs though its Community Animal Project that helps cats and dogs in poorer areas of Virginia, near its headquarters.[65] In 2008 they neutered 7,485 cats, dogs, and rabbits in that area, including pit bulls and feral cats, at a discounted rate or free of charge. They help neglected dogs and cats who are ill and injured, and pursue cruelty cases.
They urge population control through neutering and adoption from shelters, and campaign against organizations such as the American Kennel Club that promote the breeding of purebred strains"
"PETA argues that it would have been better for animals had the institution of breeding them as "pets" never emerged, that the desire to own and receive love from animals is selfish, and that their breeding, sale, and purchase can cause immeasurable suffering. They write that millions of dogs spend their lives chained outside in all weather conditions or locked up in chain-link pens and wire cages in puppy mills, and that even in good homes animals are often not well cared for. They would like to see the population of dogs and cats reduced through spaying and neutering, and for people never to purchase animals from pet shops or breeders, but to adopt them from shelters instead"
Wikipedia says that they support and use euthanasia in some instances. Like for cats with feline AIDS and some other diseases.
"they recommend euthanasia for certain breeds, such as pit bull terriers, and in certain situations for animals in shelters: for example, for those living for long periods in cramped cages."
This is not different from what people in general think.
Navagon: That and the funding of terrorists. Things like that put people off them too.
What terrorist group have they funded?