Don't worry about it.
Weight belts are NOT going to give you any problems unless you pack on an obscene amount of weights. And this is a catch-22 anyway, because the weight you'd need to strap to yourself is way more than you'd ever be able to do pullups or dips with.
You should always opt for a belt which can be tightened pretty snugly around your waist. And the more surface area the belt covers, the better, because it spreads the pressure out.
Backpacks, I have less experience with in terms of dips and pullups. But in the army, we ran 30k (~18.6 miles) with pretty substantial backpacks, in addition to helmets, rifles and vests. We also did a lot of obstacle courses with the same stuff imposed on us. I have a hard time seeing that we'd be doing this if it were known to cause back problems.
This is of course barring any problems you have already which might be worsened through physical exercise.
I have an umbilical hernia (which I've not yet opted to treat because it's not causing any problems), and I've had a couple visits to the doctor just to get some info on it.
First off, there are a large set of different ways a hernia can arise. Physical exercise doesn't usually cause it, but it can make existing herniae more protruding and more noticable.
Personally, I notice mine when doing abdominal work, but this is because mine is located at the belly button, and I suppose is subjected to some pressure when my abs are flexing.