If this is for a freewheeling bike just add a tensioner that is aligned correctly and get the best of both worlds. It still will be louder than a straight chain, but should be ok. It won't wear your cog and chainring down as much.

The "safe" deviation would depend on cog/chainring type, size, wear, trueness, etc. The chain itself will have a huge role in this, most 1/8" chains have much less latitude for side to side motion than a 9 speed chain would (as you could guess). The safe latitude is just whatever the range is that you won't drop the chain.