Speedup capacitor for compensating stray capacitance
The full voltage doesn't actually appear across R1 because C1 has to charge up, and the voltage of R1 and C1 are the same. But as C1 is charging up, C2 is also charging up making a capacitive divider (along with the R1/R2 resistive divider) so the full supply voltage never actually appears across R1.

And during all this, the direction of the voltage change (dV/dT) never actually changes so no tripping happens. For the output to trip over itself, the reference threshold has to suddenly and momentarily reverse direction as it is moving and cross the input voltage as it does so. If the threshold is moving in the same direction (either towards or away from the input) the entire time, you still get a single, clean point where the output changes.