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the resistors (and the capacitors of course) will not alter the DC response as long as the p mirrors are nor squeezed out of saturation. The resistors could help with current matching if Vref is larger than the opamp input OP.
This bandgap needs a startup circuit no matter your changes.
The capacitors in this configuration might hinder stability at high-frequency but little can be said unless the opamp gain and small-signal parameters of the PFETs are considered; stability can be insured if the positive feedback loop loses gain at high frequency