How will central banks regulate cryptocurrency, and what are the privacy implications?

Eventually pretty much as other equities or related value assets are regulated. You would need to be licensed to issue them or work with a licensed provider for issuance.

The same would hold true for trading them (on an exchange) and/or otherwise.

If there is a consumer facing element to it, you would need to provide some form of consumer protection or at the very least a methodology of addressing consumer complaints.

Banks will look at it as mostly another exotic currency and treat it as such.

The central banks of most major economies will have to struggle to regulate it as an FX per se, as it has more of a stored value association rather than currency.

All in all, central banks will say if you will play or mimic your cryptocurrency as an exotic currency, you will have to play by the Foreign Exchange rule book that they have.