I would NOT be doing deadlifts or good mornings until you have confidence that the core is strong and your back isn’t going to pop.
Your back will ‘pop’ if you don’t lift with proper form and you slack on your breathing or fail to keep everything nice and tight. Lifting stupid weights before you’re ready will also stuff you but most will be okay if they record their form from all angles. Same with the bent over row or any weight lifting exercise; form is everything.
You could do a lot worse than have a look at Rippetoe’s Starting Strength if you doubt the deadlift, squat, row and various press moves ability to basically exercise all major muscle groups. Claiming it’ll stuff your back if your core isn’t developed is just scare mongering IMO.