If you publicly acknowledge that you are accepting bitcoin as payment, beware that you will have to account for it's value on the day of the transaction. This means that if a person buys a pair of shoes at $50 and you hadn't adjusted your own exchange rate in line with the market for that date, you could end up recording more $ or less $ for that sale, and you pay tax a % of your profit on that sale.
A freelancer however could, in theory, conduct their business entirely out of the public gaze, but that would also entail your customer playing the game. If at least one half of the transaction's address is known, then the other can be found out in the blockchain. It won't identify you specifically in the transaction, but your customer may be forced to disclose who they were paying.