Are back extension exercises safe?

Yes, provided that proper technique is utilized throughout the movement, back extension exercises are safe and effective exercises that can help improve stability, strength, and endurance of the hip and back muscles.  Be cautious with these exercises and only use your bodyweight as resistance until your strength improves.  Also, be careful not to perform the movement too quickly and not to go too far into the end range of motion.  Essentially, you only want to raise the upper body until your head and back are in line with your legs and not any higher.  Seek the assistance of a qualified health and fitness professional if you are unsure how to perform the movement correctly or how to incorporate it into your fitness program.