I think much of the hate for "New" Family Guy is because many people really, really liked the original first episodes. So much so that the fan support and strong DVD sales brought it back from the dead. And upon it's resurrection, they were expecting to see more of what they liked.
And instead they got shit on in favor of people like MovieBob who didn't even like the original show.
I'll be honest here, I loved the old Family Guy. And I don't like the new episodes all that much. The reasons for this tend to be pretty much the same reasons why MovieBob holds the reverse opinion. The part of Family Guy that was interesting to me WAS the lack of good characterization. Having each character be a thin and exaggerated parody of a stock sitcom trope is what made the show work at it's core. Adding to the characters to give them depth and build a "dramatic" show defeats that whole point. Especially when the "depth" often comes lock-step with lame lowbrow humor and thinly-veiled liberal pulpit-pounding. Lowbrow humor works when the whole thing is an obvious parody, the viewer isn't just laughing at the joke, they're also laughing at the sort of person who thinks that joke is original and funny. When it's played straight on the other hand, you just feel insulted that Seth McFarlane thinks his audience is made up of those very people with terrible taste. Slapping on the liberal bullshit just throws away any good will at all. And I say that as a pretty left-leaning guy.
Look, I don't WANT my animated comedy to take political stances. I don't even like the sorts of people who do that sort of thing in real life because they tend to be either naive idiots or manipulative assholes. That's what makes South Park generally funny even when they address political topics. The ability to understand that we really shouldn't take some things too seriously, and people who do that are wankers.