While WoW has ALWAYS had a problem with rampant elitism, I don't think it actually comes into the equation for LFR. Mythic raiders get the prestige of having downed mythic content. They don't need the added ego boost of laughing at LFR players. I doubt Mythic raiders even know LFR exists most of the time unless it somehow impacts their Mythic runs(like having to farm LFR for Titanforge upgrades. Worst. Design. Ever.)
Mythic wannabes will probably tell people that LFR should be removed. Generally this mentality comes from people who WANT to feel like a mythic raider, but don't actually do mythic content. It's the middle-range player who thinks that they are somehow made better by shitting on people who don't play at their level, even when their level is only normal/heroic. These are the worst parts of the community right there.
It's generally the opposite. As I said above, it's usually NOT the mythic raiders lording over lesser players. Mythic players generally only care about clearing mythic content, and don't give a rat's ass what everyone else is doing unless it's also mythic content. By the same token, LFR players generally aren't jealous of Mythic players because mythic content isn't even on their radar. They're "casual" remember? The complete opposite of the Mythic lifestyle.
No, the entire thing boils down to middle players who can't stand the idea of anyone playing differently than them.