Got to be honest, I've never known someone wanting to do that. Yes, I would expect there is an app out there that removes the 'rich notification' element, but I'm afraid I don't stray away from Hangouts, so don't know what it would be...
I'll double check next time I get a text, but from what I remember if anyone got hold of my phone and pulled the notification bar down, they'd be able to see any un-read texts I had. This is on the lock screen by the way.