If the output (not input) of MCP1501 was connected with VCC of other chips and each chip had 1μF to ground then yes, you had 3μF on the output of MCP1501, which is more than permitted.
Simple solution: use other reference. Any strong reason to prefer this one?
Weird solution: try to compensate it. Run a direct capacitor from OUT to FEEDBACK and connect both pins to the load (and its capacitors) with resistors. This is utterly undocumented, no warranty and so on, but it ought to work, I think. You will certainly need to see how much current the FEEDBACK pin sinks and size the series resistor accordingly, to avoid excessive error.
I hope to convince you with this to try the simple solution instead...

edit
I actually have this chip, but in 3.3V. I played with it, it's just a reference plus an opamp, connected together in the most obvious way. There is a bizarrely incomprehensible "block diagram" in the datasheet, it makes no sense to me, I think it can be ignored. FEEDBACK drives an internal feedback divider of the opamp and sinks not entirely negligible current. I also tried putting various things in the feedback loop of the opamp (NPN emitter follower, even LM317 IIRC) and it seemed to work as expected, although I'm not 100% sure if I checked for oscillation now that I think about it.
I wanted to use this as a single chip (+ external transistor) constant current regulator, but the project never progressed past a crude breadboard proof of concept.