I really wish that Respawn would make some kind of statements about 1) forced crossplay in mixtape and 2) the Steam Cfg situation that PC controller players are exploiting.
Most of the "jumping high" stuff that you see can be executed on controller on console, it's just a matter if putting in the time practicing the techs. I can't be bothered, but they are available to all. If you're curious, you can start by looking up tutorials on mantle jumping, supergliding, and fatigue wall-bouncing.
I don't have anything to say about gyro, but I'd imagine it could help some with advanced controller tech, since much of it (i.e. mantle jumping) depends on how quickly one can look up and down. The weird strafing stuff you're seeing is only possible on controller by exploiting Steam Cfg files to make the controller send WASD input to the game.
I agree that it's feels unfair to play against all of this extra movement tech in our console mixtape lobbies. It is really fun, though, when you 1v1 someone doing that stuff and kill them anyway because so many of them cannot do it all and actually aim well at the same time. A well-considered PK shot can often send them back to the spawn room. It's one of the very few times that I will t-bag players.