Cash is only private if you never put it in a bank.

But if the reason for taking the payment is legitimate you're going to have no more problems with Bitcoin than you will with cash in this regard.

If your reason for taking the payment is illegal then I agree, Bitcoin puts you at some greater risk. But if that's you're point then perhaps you should be clearer. Bitcoin can be dangerous to use for criminals because it's more traceable. If your use is legal, it's no more or less dangerous than cash.