I think that this is the big problem with LDO regulators. Their stability is highly load dependent. When I have used them, I performed stability tests (injected disturbances), varying all relevant component values over a wider range than tolerances would account for, in the actual layout, and using several different regulator units from different production batches. This means that the board layout had to include provisions for alternatives.
But I always worry about the generality of the solution I arrive at, especially if the regulator or load undergoes any significant revision.