I never get the hate for great players. There were plenty of people here who hated Peyton Manning, before he came to the Broncos (I could bump threads, if anyone needed proof).
I respect the heck out of Tom Brady. I don't believe he is the GOAT - but he's definitely in the conversation. Granted, he looks a little ridiculous in the gif in the OP. But how about that stat they showed during that same game? He's something like 69 out of 71 on converting 3rd or 4th and 1 in his career. That's pretty crazy! He may not love getting hit; but he certainly hasn't lasted this long being terrified of it.
On the other hand...
He looked like a whiny, little diva on the spike after the refs granted the 49ers the time-out. They were signalling for it, right across the line from him, a good two seconds before he snapped the ball. If almost any other player spikes the ball in that situation, it's unsportsmanlike conduct (Peyton could have probably gotten away with it, too).