Can the OpAmp be safely removed from the Twin-T notch filter?
Both opamps in the original circuit are wired as voltage followers &mdash; unity gain buffers. They have very high input impedance and very low output impedance, which means that they isolate the circuit on the input from any loading by the circuit connected to the output.

As you have discovered, this means that the input circuit performs closer to its theoretical predictions, and you have more freedom to use the output signal any way you wish.

Removing those opamps means that everything now depends on everything else, making prediction of the circuit performance that much more difficult. You CAN make the circuit perform the same function as the circuit with the opamps, but there will be undesirable interactions between circuit parameters, input source impedance and load impedance.