Problem with digital potentiometer [MCP41010] in Op-amp Amplifier
The digital pot can have significant capacitance from its analogue pins to both ground and the internal digital clocking input. This means two things: -


high frequency gain is high and op amp noise gets massively amplified
when clocking in data, you get noise injections to the inverting input.


With your non-effective offset control, you will get very little noise injected because the digipot is in series with a resistor, R28.