If I am not mistaken no single block in the public tangle is ever fully confirmed. What exactly determines the treshhold when funds are actually received, making the transaction relatively irreversable and "complete" in most peoples eyes? Does the receival automatically implicate the complete nature of a transaction or not, considering this happens online and thus on the main public tangle? Thank you.
The current situation: The Coordinator is issuing transactions and these transactions are connected to branches of the tangle. These transactions are called milestones. The full-nodes are still validating the transactions. So, if the milestones are breaking these rules, the milestone is not valid. Mobilefish recorded a fantastic video and explains this in detail.
Eventually: It depends on the use-case. It is a matter of risk management. You could also say that your transaction is confirmed when the RWMC is 51%. Another issue might be a network which is partially offline. IOTA also works if your network is not connected to the main-tangle all the time. So, you could also say a transaction is confirmed when it is confirmed in your sub-tangle, even if it is not connected to the main-tangle. Depending on the transaction value and the size of the sub-tangle. If you have a small transaction value, the chances are little that somebody is attacking your sub-tangle which is currently offline. When your sub-tangle is online again, it is likely to get confirmed by the main-tangle. But you also need to connect it to the main-tangle via transactions.
As stated by others, in the current tangle the entitiy called "Coordinator" issues so called "milestones" every 2 minutes or so. As every transaction must reference two older transactions (normally "tips", meaning unconfirmed transactions), the milestones references one transaction and the previous milestone. Your own transaction is considered valid, meaning the funds can savely be considered received, if it is referenced directly or indirectly by a milestone. This takes about 2 minutes.
The original consensus mechanism described in the whitepaper is not implemented yet but probably will, or some variant of it, at some point in the future.