How to isolate the microcontroller from power source?
If the microcontroller is running with 3v and the shift registers are at 5v that could be a problem.  Per the spec the shift register chips want to see at least a 3.15v min high logic when their supply voltage is at 4.5. (A 5v supply would require even higher logic levels).  If you power the shift registers with 3v that should make both compatible.  Is there a reason you cannot use the same microcontroller power for the shift register chips?