What's the purpose of the resistors and capacitors in this latching push button circuit?
First of all 3.3V should be enough since that MOSFET has a very low gate threshold. You would maybe touch up some resistor but in principle it should work as-is.
The 'series' capacitors are used to transform a level into an edge, as differentiators. When you change polarity they briefly conduct while changing charge and that's developed in a potential by the associated resistors.
The other 100k resistors are simply pullup to hold the lines to a definite state since MOSFET are, essentially, open circuits when seen from the gate. Also, they develop the capacitor pulses.
I presume the auto-on/off switch chooses the state when you power on the circuit, the 100nF capacitor in that case gives the inital pulse.
Of course the top MOSFET runs the load while the bottom one latches the gate of the top one, if it wasn't clear. Hope it helps