Which podcast apps support private podcasts?

iOS podcast apps that allow you to add private feeds:

Apple Podcasts (video demo), Overcast (video demo), Pocket Casts (instructions here), Downcast, and Castro.

Android apps that allow you to add private feeds:

Castbox (instructions here), Pocket Casts (instructions here), Podcast Addict, Podcast Republic (instructions here), Player FM (register for an account first), Dog Catcher, Beyond Pod, Podcasty, and PodKicker.

Apps that don't support private podcasts:

Spotify, Google Play, Stitcher, iHeartRadio, Acast, Podcast App, PodcastOne, DoublePod, PodcastHD, and Podcast Guru.