The sim with the 7805, a p-jfet (it is picky, however), the LM308 (with its compensation inputs) and a high ESR capacitor works stable it seems, the issues start with 317+bipolar/mosfet+modern_opamp. Would be great to find a stable solution with easy to get parts..
The p-channel JFET should not be tricky at all. Nothing prevents the operational amplifier from driving the regulator directly except its output voltage range, however if the current is high, which will not be the case with a 317 which only requires an adjustment pin current of microamps, it will compromise the precision of a precision operational amplifier.
The regulator combined with a low noise operational amplifier, which is almost certainly faster than a 308, requires external compensation for stability. I add a lead network (two capacitors and one resistor) to the top of the resistor divider and a lag network (also two capacitors and one resistor) from the operational amplifier output to the inverting input, but not all of the parts are likely to be used. Values are mostly dependent on the regulator's frequency response combined with the output capacitance, so the output capacitor also significantly contributes to the frequency response but the recommendation for the regulator is suitable. Since the regulator's frequency response is poorly defined, I tune the frequency compensation empirically which is easy, and then the frequency response of the regulator can be calculated if necessary. Network analyzers have always been expensive luxuries for me.
I know of a much more sophisticated form of frequency compensation for difficult loads involving a feedback network with less than 90 degrees of phase lag, which increases the frequency margin, but it has not been required here.
Note that using a lower noise and faster operational amplifier will generally *not* lower the noise, because noise is dominated by the reference even when a low noise reference is used, so using a relatively noisy 308 is not a disadvantage. I last used a low noise LT1007/OP27, but in retrospect an LT1001/OP07 would have been just as good if not better, and easier to frequency compensate. A precision improved 308 part like the LT1008/LT1012/LT1097 might be better yet because of external compensation or overcompensation support. Of course these days there is no shortage of suitable precision parts with low flicker noise, low drift, and high gain.
High frequency performance is dominated by the output transistor or regulator and there is something to be gained there with careful design and a faster operational amplifier, but usually this is irrelevant.