Is it safe to use two power supplies to two different circuits independently sharing the same ground?
Yes it is safe, as long as you keep the current pathway between the supplies high impedance, if you design the circuit wrong you have a potential for voltage to flow from  the higher voltage to the lower one. I've drawn a simplified circuit diagram, you could simplify your loads on each supply as R1 and R2 and whatever circuits between them as R3. R3 has to be acceptably high, meaning it could be 1k if that is acceptable for you. If the voltages are the same then you could have a low impedance between them, but voltage supplies are never quite the same... 

A good engineer will be able to circuits and be able to simplify them into simpler circuits to answer questions. A microprocessor or IC can be thought as a changing resistor, if you know what your current draw is and the voltage you can find the load value of the resistor. 







simulate this circuit &ndash; Schematic created using CircuitLab