I don’t have a response for you, but I’m having the same problem. When people put the password into a password protected post, the WP login page comes up.
If you open a new tab or just keep trying different things you’ll eventually get in, but this causes most people to just give up. They try the password once; it takes them to the WP admin page. Login? Password? They don’t know what to do. They try again; it happens again. They give up and don’t visit the blog anymore.
What’s up with this bug? Anyone? Is it theme related perhaps? I’m using Woothemes Typebased.
https://amityeric.net/