Many LDOs are inadequate to the task of attenuating HF
ripple, as produced by swotching supplies upstream. A
smaller number are meant specifically for this (HF PSRR).
You need a high loop BW if you are getting DC PSRR by
loop feedback, and many older LDOs just are too slow.
But maybe this is telling you to pay more attention to the
incoming supply ripple voltage, or the uC's transient
demand current (w/ any sourcing inductance or poor
quality close-in LDO supply decoupling).
Grab your 'scope and go hunting for "not right".