On the topic of "How conversant do you want to be with bookkeeping as a business operator?": there is zero value in having you, personally, write up that you spent $4.76 on a coffee at Starbucks. That is an actual thing your business requires someone to do; it should not be you.
Should you know what double-entry books are? I think you can safely pass that off as "implementation detail."
Should you know how to read a balance sheet and income statement? Yes. That's a really critical job function. Are some of the individual entries a little opaque if you know nothing about bookkeeping? Possibly. Member Contribution / Member Drawing come to mind.
There are some less-bookkeeping more-accounting topics which I think software entrepreneurs would be well-served by being better at. "Revenue recognition for SaaS businesses" is a decently good example. I see that bite smart people all the time.