Tubex (
https://itunes.apple.com/at/app/tubex-video-music-player/id1164818253?mt=8)
dose not allow you to sign in. → no subscriptions visible. And it plays in the background but does not offer PiP.
I still use ProTube but indeed for background playback this doesn't work anymore when you have to select 'the alternative player'within ProTube when searching for a video.
The Tubex one you mention in another one then I downloaded a few months ago which had a red icon and has PiP and still works here but is not in the App Store anymore.
Some alternatives (although not perfect and not ProTube) which are currently in the App Store are:
Musi
It has: background playback, login, no ads (banner or video) but
only if you do the 3.99 dollar in-app (once) otherwise you will get loads of full size video ads and a banner, it has Slide Over/Split View (however Slide Over looks pretty bad),
It lacks: PiP, Chromecast, the homescreen and the rest of the app is mainly focused on music while you can also perfectly watch other things with it
Evercast /
Streamy (both apps are from same developer)
It has: background playback, login, Pip, Slide Over/Split View, no ads (banner or video) but only if you do the 3,49 euro in-app (once) otherwise you will get full size ads and banners.
It lacks: Chromecast, it's
not in the US App Store but is available in certain countries in Europe