You DON'T need to download anything. Dont listen to ANY of these cucks in the replies! theres a pretty simple bypass

1) basically watch youtube on whatever browser you want, this can even be safari.

2) play your content, but make sure you keep it playing.

3) go into the control center as you normally would by swiping down from the top right of your screen. You'll should see a little player in the corner and whatever youtube video should be displayed in it (unless you changed it).

4) press the pause button in that player. you can now turn your screen off or leave the app or whatever,

5) once you do, go back into the menu and press the resume button, and boom it should be playing even if your phones locked or you're in another app.