There's levels to this.
If you criticise the player for a performance that's one thing.
If you heavily criticise him, that's another.
But when you (not specifically you) start calling him shit, talk about how awful he is, make every attempt to say how awful he's always been, state how willing you are to get rid of/sell him, and whatever else, then that's another level.
Read through this thread since the loss today and you'll see that there's some severely emotionally fuelled bile aimed at him. This is the hate. This is what drowns out all reasonable critique. This emotionally charged anger is what establishes the culture of abuse.
This might seem similar to what is said at a game, but this is worse online. Because at a game there aren't going to be many people who hear you, nor does it linger past it being said. Online, not only does it last forever, but there's potentially hundreds, thousands, maybe even magnitudes greater of people that can read it. This starts the loop of people dishing it out, all in one concentrated space. The more posts there are, the more people that can see it. I can assure you it's the same on twitter and facebook. The negativity grows. Look at this place after a win, emotional negativity is drowned out. But after a loss, it's cultivated and grows and grows. People see this and repeat what they read here or wherever either here or elsewhere. With this abuse and hate, there's always going to be some stupid or legitimately racist people that feel it's appropriate to go too far. And with how prevalent it is after a bad result, that tiny percentage of people that have that mentality are a larger number of people than we realise.
It's not just City fans and it's not just Sterling, but when people can't control their emotions things always have the capacity to get out of control.