Why the capacitor doesn't see R1 and R2
The op amp together with R1 and R2 is an inverting Schmitt trigger. As long as V- is smaller than R1/(R1+R2) *VDC (VDC being the operating voltage), the output will be +VDC. As soon as this limit is reached, the output voltage will change to -VDC and will remain there until V- will drop below - R1/(R1+R2) *VDC.

In both states, the output of the op amp will be a nearly perfect voltage source and will charge or discharge the capacitor with a time constant of tau=RC. 

The values of R1 and R2 determine the levels where the switching will occur. However, they have no influence on the time constant. 

P. S.: The amplitude of the output signal does not depend on R1 or R2 but only on the operating voltage.