No one says you have to stop exercising. You have to stop doing the stuff that hurts you. The kind of back problems you're having now sound like something that's going to get better with time, probably. Nobody, and I mean nobody, truly understands the back. And what works depends on what the anatomic injury is. My wife has a bunch of compression fractures from HS and college gymnastics. Yoga works well for her. I have spinal stenosis and get relief from a posterior pelvic tilt/ab strengthening. Yoga, with it's hyperextension of the lumbar area (down dog for example) is bad for me. It is not unusual for relatively minor movements, without weight, to trigger back problems. My problems were triggered by working on my knees with my back hyperextended--stuccoing the insulation around the foundation of my bathroom addition, although a lifetime of overuse led up to it.
Re crossfit and other work out regimens--at this point no one knows what the long term impact will be. My wife didn't know that being a gymnast would leave her with back problems years later. If you want to stay fit for life you have to protect your body. Unfortunately, we don't have a good idea of how much we can do when we're young and not pay for it as we get older.
Good luck.