You can do an offline transaction, but there's no way to prevent double spend until it's online. If you gave some crypto to someone offline, you could double spend it until the recipient is online and publishes the transaction.

AFAIK, the blockchain is online, so I can't conceive of a way for an offline transaction. I suppose you could write down your wallet service and/or ID on a piece of paper, then when the store goes back online they trustfully transfer the digital money, but even then one of the parties must be online.

My perspective: I don’t see bitcoin replacing fiat anytime soon, so for day-to-day transactions, cash works all good! No need to replace it completely. They can coexist.

In the scenario you mention, I’d just reach for cash.

However, as a protocol for payments/value in the digital world, it’s very compelling.

If we are aiming to re-think currencies and use cryptocurrencies as the new building block, I feel like it should handle these cases, otherwise we will need to re-do the whole thing again in the future. I'm too lazy to do this multiple times.