I don't understand how this works. Where is the output being tapped off? From the Ref node, or where C3 is?
The common (top) rail, with C3. Implication being, start with any old shunt circuit (note that R2 may have a companion divider resistor below it, REF to GND), add R3 in series, and C3 can then be whatever value as needed. Pull-up not shown either.
I am surprised the app note does not mention anything about output cap ESR. If you use an output cap, it should have some reasonable ESR that is NOT too low. Sounds counterproductive but this isnt the only application like that. A boost converter with some reasonable ESR that is NOT close to zero becomes more stable. That's because it gives the feedback a little wiggle room to level off without being too strongly affected by the clamping action of the output cap.
Note that relevant ESRs are much higher than most capacitors will have. As just any other op-amp circuit, an "isolation" resistor of some 10s of ohms is typically required.
Less ESR may be required for values near the instability region, than for values in the middle of it; the region also varies with bias current.
The other "best answer" is this: if you need bypass for filtering purposes, TL431 simply isn't what you want, get a less noisy ref instead! LM4041 say, or various other choices. (Note that LM4041 is variable, like TL431, but its REF is referenced to "cathode" instead, so the divider ratio is upside-down!
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).
There are also refs available, with pass type outputs (lower current consumption), and with internal filtering nodes (so you can tack on a bypass cap there, and the output pin is a voltage follower from it).
And, the related "non-answer": don't inject AC currents into your REF node to begin with! If you are, you're probably doing it wrong. A non-answer because it could require significant circuit revision, but revision that is nonetheless worthwhile from a design practices standpoint (if not worthwhile/applicable for a particular mostly-complete design).
For example, last time I needed 2.5V ref, I used a TL431, no bypass, and passed that straight into the MCU (AVR-DA) VREF pin (12-bit ADC). Readings are stable and accurate.
Tim