The f7/f2 bishop sacrifice is often seen in the Italian game. To avoid it...castle earlier. In the position you posted I woud get my rook onto the now open f-file and step the king back to g8.
He has given you a bishop for a pawn. You will lose tempo having to move the king again but he has gifted you an open f-file bearing down on his KBP
Only patzers sacrifice their bishop in this position. After the sacrifice white has only 1 (!) developed piece, while black has 3 developed pieces. White cannot attack to take advantage of the sacrifice, and the black king will be safe after artificial castling.
In that particular position I would take the bishop. Because afterwards you can easily move your rook to f8 and then your king to g8, accomplishing essentially the same purpose as castling.
Black simply grabs the bishop and thereupon castle artificially. Clearly unsound sacrifice.
Now I know the King is to recapture here, but with the recapture castling is impossible of course, one of the King's protecting pawns are removed and the King is now vunerable. How should one continue so as to not fall prey to these sorts of early piece sacrifices to flush out the King?