Is privacy compromised when using privacy-respecting apps on non-private operating systems?

Yes - as far as I know. I’ve seen mentions of this “secure path” only in two contexts: playing movies, and virtual machines in server rooms.

EDIT: even then, the one who is usually protected is the hardware manufacturer: they hold the encryption keys. Unless you install the encryption key into the hardware yourself, it’s not your data that’s protected by the hardware path. PureBoot is the exception: your encryption keys protect you from someone who tries to gain access to your stuff. Not hardware manufacturer’s keys, and not movie copyright group’s keys.