The dynamic lumbar flexion that is caused when getting up off the floor, when doing 2 legs at the time, can cause pain and injury to the lower back in problematic backs and even in normally solid backs. So if you get low back pain regularly, and do burpees, pay attention next time when doing them, and see if they contribute to or even cause it.
It’s mainly when doing the 2 legs at the time, jumpy version, and any version where unable to maintain the natural curve of lumbar spine. If you can do them one leg at the time, and keep your back decent, then go ahead.
Exercises aren’t inherently bad, they are only bad if they cause harm.