I think with Angry Birds it's more a case of what TV Tropes calls Hype Backlash. It's one of the most popular and best-known smartphone games, and it has a ton of really enthusiastic fans and merchandise for those fans. It's hard to escape even if you don't own a smartphone. I think a lot of the "controversy" is just that people are sick of hearing about it - similar to most of the "controversy" Pokemon had at the height of its popularity, where it was largely parents who were sick of spending so much money on the merchandise for their kids.
Also there's probably some animal rights group somewhere that thinks the idea of hurling live birds as projectiles - even ones as cartoonish and unrealistic as the ones depicted in the game - is promoting animal cruelty or whatever. The same sort of people who complain about Pokemon as being a fantastical version of cockfighting.
For the record, I love playing Angry Birds on my phone but not enough that I'd buy an Angry Birds plushie or t-shirt or anything. It's fun but I don't understand the level of obsession that some people have with it.