Some apps are purposely limited in terms of CarPlay availability, generally for the sake of safe driving. This includes video playback apps such as Netflix or YouTube.
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This simple add-on, compatible with all devices that support TrollStore (namely iOS & iPadOS 14.0-15.4.1 devices and some 15.5 betas), allows users to search for and watch YouTube videos via the infotainment system in their CarPlay-supported vehicle’s dashboard.

The app you perma-sign looks and feels a lot like YouTube, but isn’t the official YouTube app. It has been modified to not only support CarPlay, but also to block ads and sponsor segments so that you can focus on what matters most to you.

CarTube