Pops are always a result of the switch suddenly changing the DC conditions in the circuit. This can be tiny changes ("ticks"), short, small changes ("clicks"), bigger, longer-duration changes ("pops") or slower, but large changes ("thumps").
The commonest way to get transients like this is to switch the end of a capacitor. Capacitors block DC, but leak down if one end is left open. The solution to this one way that transients happen is to terminate each end of the cap in the DC condition that it will have when connected, so it cannot leak down when open. The pulldown resistor is a special case of this, where the "inside" terminal of the cap is held at a DC voltage, the "outside" terminal is held at 0V, so no leakdown happens.
In midair switching, it's common to add a pull-somewhere resistor to hold both ends of the cap at a non-changing DC voltage. Sometimes you can do this by putting a large valued resistor in series with the cap and using the switch to "short out" the resistor.
Your schematic does not show in your post so I can't advise on specifics. If you can provide a link, I can help more on this.
One thing that might help is to get out your meter or oscilloscope and watch the output of the first opamp after the switched capacitor for what it actually does when the switch it changed; does its DC level change or does it just do a blip-and-return? That might provide clues.
