Adding a potentiometer before or after a passive filter
Is it safe to assume that a potentiometer after the filter will not
  alter the frequency response significantly?


If you put the pot before the circuit and it is a high impedance pot then mid-band and mid-position, you will have a fairly high impedance pot loaded by R4 and R5. This can noticeably affect things so, in this position, the pot ought to be 10k i.e. much lower than R4 or R5.

If you put the pot on the output then it needs to be high impedance. This is because the series resistor R6 will not be unduly loaded by a high impedance pot such as 100 kohm.

Two scenarios but different pot values.

A 50k pot would best suit being connected at the output.