Sterling divides opinion because he's a difficult player to understand.
I'd put Rodri, Jesus, Walker, and Zinchenko in similar contexts. Gundogan was formerly misunderstood too.
All these players are exceedingly good with the intangible stuff. For starters, they're all brilliant as far as off the ball movement is concerned. They're also very good at doing the safe stuff that Pep likes. Rodri reads and controls the game brilliantly. Walker is positionally excellent (barring brainfarts) in defence. Zinchenko has excellent awareness. Jesus opens up space and defends excellently from the front. Sterling stretches defences and exploits space extremely well. There's more too for each of them.
What all of these players don't do, is spectacular things with the ball. Nor do they often to stuff that passes the famed 'eye test'. Rodri doesn't play 20 throughballs a match nor does he fly into tackles. Walker is limited in possession. Zinchenko doesn't make great attacking plays nor make divine defensive interventions. Jesus doesn't score every chance or make 100 runs into the box at every opportunity. Sterling takes this to the next level, as he doesn't look conventional at all, failing the 'eye test' at every opportunity almost. Gundogan's only getting his deserved praise because he's more aggressive in the tackle and scoring more (the stuff that's easier to see), but a lot of his other abstract elements have always been there.
@Dax777 has spent the best part of three seasons telling everyone Gundogan is the smartest midfield defensive player in the team for a reason.
Assuming a team has 50% possession and that keeper involvements are negligible, that means that on average every outfield player has about 5% of the game in possession. That means they have about 95% of the game without the ball. That's the bulk of the footballing iceberg. Pep loves the players that give him the 95% of the game to the level he loves. It's why he was so persistent with the aforementioned players when everybody wanted them sold/dropped, and why he continues to play them now. It's this (lack of) element that's been what's been keeping Foden out for so long, but now he's starting to understand it he's flourishing.
Not that the other 5% doesn't matter, nor that the criticisms of these players are invalid. Sterling could be doing more with the ball for example; he'd say the same! But these criticisms are being prioritised over other less obviously visible elements that are clearly being either misunderstood or wilfully ignored, when to anyone who's taken a moment to try and understand Pep's methods will realise that they are in fact the most important part of the whole shebang.
