what does the reverse voltage rating on an optoisolator mean?
If you connect the LED anode to the same voltage as the op-amp rail, it will be impossible for the LED to be reverse biased at all.
If you use a lower supply to the LED anode (5V, say), then you need to limit the anode-cathode voltage to no more than 5V, or 10V max for the anode. You could do this by using a reverse-connected diode across the LED which will limit the reverse voltage to one diode drop, about 0.7V for a ordinary switching diode like a 1N4148.
The issue you’re actually encountering is that the op-amp won’t swing any higher than VDD-2V. This is leading to leakage current on the LED leaking back to the op-amp, which can only swing to about 10V, so the LED is still being biased at about 2V. LED Vf is 1.3 ~ 1.5V.
Add 3 series diodes to the LED (1N4148 type is ok). This will shift the forward bias voltage down by about 2.1V, resulting in an overall forward voltage of (1.3~1.5+2.1) = 3.4 ~ 3.7V.