Can the diode be ignored in this Op amp circuit?
simulate this circuit &ndash; Schematic created using CircuitLab


When Vi > 0 the diode conducts and shorts out R2. Stability will be reached when Vo = -0.7 V (for a real Si diode) and at 0 V for the ideal diode in the question.
When Vi &lt; 0 the diode is reverse biased and is effectively out of the circuit. \$ V_O = - V_I \$.
The circuit when created with a real diode is an imperfect (due to the -0.7 V output) inverting half-wave rectifier.




From the comments:


  Doesn't an op-amp force the voltage on both inputs to be the same?


Yes, in negative feedback configuration. 


In Figure 1b we have a current flowing through R3 tending to raise the voltage on the inverting input. This will cause the output to swing negative.
When the output swings to just below zero (or just below -0.7 V with a real diode) the input will have been pulled down to 0 V and will match the voltage at the non-inverting input. The output will stabilise at that point.