Shift work per se shouldn't prevent you from being in a band.
I worked shifts for over 30 years. Not just earlies and lates either; these were earlies, lates and nights in various patterns over the years. For 20 of those years I was in a band which had three other shift workers in it and we made it work. I would often takes a night offers annual leave/swap a shift/re-arrange finish times if we had a gig and the others would do the same. I don't recall one occasion during the bands existence where someone failed to turn up. My job was probably the most unpredictable in that I could be held on duty without notice, but I just planned around it.
@Horizontalste - I was working your shift pattern towards the end of my time and it was probably the most awkward, but it's doable. Two earlies, two night four days off gives you options. You might not be able to gig every week, but second early and the first three rest days out of every cycle are usable. Hope you find something.