Why does this current limiter circuit oscillate?
The negative feedback loop of the left Op-Amp goes thru the FET and second Op-Amp, which makes analyzing stability a nightmare (and stability itself intuitively improbable).

There is hope you could damp that left Op-Amp by adding a series resistor on the negative input, and a small cap between output and negative input. For a start try R = 1/(6.f.C), e.g. C=100pF, R = 22k. Increase R if that has no effect.

Update: if you try it, please tell us the effect!