All of them, oxygen, propane and acetylene have their own special dangers. Though acetylen is the one that would be the first I would secure with a flashback arrestor, since it can decompose exotherm inside its bottle, heating up and probably explode if not cooled from the outside or thrown into a garden pond or swimming pool, - which would be my first choice in this case.
Surely, exploding propane hoses arent nice either, I guess. The oxygen is at 4 bar, the propane at 1bar right now, so it is nearly impossible to get propane into the O2 hose. One thing to consider: a burning O2 hose burns violently with white flame - then it is a good idea to shut the O2 bottle quickly
One thing I am really aware of is, that the O2 bottle can't keel over. This is told to have happened in a shipyard nearby, a large O2 bottle fell off a truck, the valve broke and the bottle shot like a rocket into the air and was lastly found on the other side of the minor fjord.
In another similar case it shot a hole into a brick wall. Well oral traditions, but believable.
On the other side in the 70-80's I've never watched anyone using flashback arrestors at all. You just knew what to do and what not to do.