Why did he tell you to avoid it? Not trying to be a GP here (not qualified, and all that legal junk), but if you complain about 'back' problems, their method of solving the issue is "don't do anything that might cause pain". Context is everything here. So If you just had back surgery or an acute injury to the back, then that would be a no brainer, as well as visiting a PT to rehab it.
Fact: Avoidance never solves underlying issues. Take gravity for example... Sucks sometimes, doesn't it? But what would happen without it? You literally degrade. Look at what happens to astronauts. I bet they feel pretty cool at first (in space), until they get back to earth and realized just how hard it is to adjust to the constant force that keeps them healthy.
What happens when you avoid phobic fears? You strengthen them. What happens when you apply ERP and face them? They weaken and you become stronger mentally.
What happens when you quit working out? You become weaker. What happens when you work out? You become stronger, or at the very least, slow the degradation of age.
Anyhow, as with the post above, axial loading needs a context. Even more, a context to your situation. Maybe get a second opinion from a sports therapist, if sports/athleticism is currently part of your lifestyle.
Otherwise, you will want to ask your GP himself what he means by it. Ultimately that is probably the only real advice, is to talk to him about what that exactly means and how long he expects you to avoid such and such for. That is, after all, what you pay him for.
