You can apply a favorite component to a public app. If a user is not signed in, it will just ask them to sign in. Like I said, I think there is a bit of a bug here. If you go back to your list and activate the favorites bar, then you will see the column in the table. Likewise I would expect the column to show as long as you have a favorites component active on the detail screen. It should still record favorites normally, but I assume you want to use the column for filters or an IF column?
I think this is something the should be submitted as a bug to glide. I think you should at least be able to see the column with your use case.