op amp current source oscillating
The op-amp's capacitive load drive stated in the data sheet is 15pF giving rise to an overshoot of 30%. Yes, you can improve this by using a series resistor to drive the capacitor (The MOSFET is about 2 nF) but you are still driving capacitance within the closed loop feedback network and that makes adding a resistor pointless - you just shift the phase further and make it oscillate at a lower frequency.

In a closed loop situation like this you have to look at the op-amp's open-loop gain and recognize that it is never ideal and might have a phase margin that is quite poor at high frequencies. A poor phase margin means that negative feedback is close to becoming positive feedback and an extra bit of RC filtering (due to the gate-source capacitance) can easily tip the balance from stability to oscillation.

You need to put a capacitor from op-amp output to the inverting input and put a resistor (try 1 kohm) from that input (pin 4) to the feedback point on the current sense resistor. You may be lucky and get the bandwidth you want but there is no guarantee.