Personal preference, but I don’t rely on the safety. Most safeties do not lock the firing pin. Some safeties lock the bolt as well as the trigger, some lock the firing pin, some lock both, some allow the bolt to open whilst on safe, some have a middle detent which keeps it on safe but you can open the bolt, others you have to push to fire before you can open the bolt.
If you are concerned the bolt getting snagged on branches and opening the bolt and dropping a live round in the bush, I suggest that is the least of your problems. A rifle getting snagged in the bush is a sure fire way of making a rifle go off.
If you have a round chambered and you are crawling through bush the rifle should be in your hands and totally under control. Besides the only reason that I can see for having a round chambered and you are pushing through bush that could snag the bolt is because you are expecting a charge from something big and grumpy.