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Depends how it is set up - but full privacy is very difficult.

in a way, it is, as everything is registered on-chain, but you do not have to link your identity to any of your accounts, you can use several accounts for different purposes, use a VPN to connect from different IPs, etc.
So although anyone can check your wallet and know your assets and transactions, you have no way to directly contact the owner if he/she wants to stay anonymous as there is no email, phone, or anything to directly establish contact unless he/she wants to do so.

That's the case now... but I assume we're only one corporate breach away from linking people to their BTC wallets.