how much is it safe to common-ground power supplies?
You need a point where the two power supplies connect, and most of the time this is the ground of both supplies. If you don't connect them they will "float" with respect to each other, meaning that the ground (or any other level) of the second supply doesn't have a defined level with respect to the first.
If they're not connected by a common ground no current will flow from the output of one circuit to the input of the second, since there will be no closed loop where the current can flow back.