mosfet, shift registers grounding issues

If you are afraid of burning down, it's a must to use potential isolation.
A very convenient way you might find with SSRs (Solid State Relays). Most of them have built-in optocouplers but mostly switch only AC using triacs. Using triacs with DC would be very complicated - possibly you switch once on and (if power lasts) never off.
So you better use optocouplers. I guess you can get such things (assume you are German) from Reichelt (ILD 74: Optokoppler =MCT6 =CNY 74-2 bei reichelt elektronik). There are two independent couplers in each case. This would be the best way do get a galvanic isolation between your low power electronics and the power part. Of course you need a separate power supply for the coils (and don't forget the diodes in parallel to them).