Some input current is needed, but if the source driving the op amp has a reasonably low output impedance, the op amp input current will not be a problem. It can be a problem if a large valued feedback resistor is employed. High values of input bias current can result in output errors.
Also, the input differential is quite small as well, but not zero. A good text on op amps can explain this in detail. I recommend reading peer-reviewed texts, then ask a specific question here if a point made in the text needs clarifying.
By the way, the input current is not "parasitic". The voltage differential could never develop unless charges are transported through the b-e junctions. Current is needed to obtain the diff voltage. But good bjt devices have a low input current. When the circuitry is designed right, the input current produces an error not too severe.