I am also running TurboTax 21 (Premiere) on an M1 MacBook Pro. Had the exact same unfortunate experience. Installed it, updated it, downloaded state, brought forward last year's return, finished ... and then it crashed and won't restart. I rebooted. I trashed the app and as much of the supporting files as I could find (tho there may be some others mentioned here I have yet to delete). I restarted, emptied trash and reinstalled. No go.
I called Turbo tech support. Very nice people. 45 minutes later, they were stumped. (By they I mean the tier 1 person who first answered my call and then the tier 2 person they escalated it to.). FYI, neither of them knew that Apple now has an M1 non-Intel computer! One did read off the system requirements, which they said required an Intel processor!!!! Also, the tier 2 expert said, "to delete just drag the app to the trash". When I suggested there might be supporting files in the system, they said "no. There's just the app". Very telling since I found at least a dozen files that had been installed the same day, most with the text 'turbotax' in the name.
Disappointed and hoping Intuit fixes this!
