Improved method of instrumentation amplifier input noise and RFI filtering
If the EMI is at a frequency within the amplifier's bandwidth, then it will process it like a normal signal, and it will end up in the output. You might have other unpleasant surprises, like CMRR degrading at HF so common mode noise is not rejected that well, or intermodulation, slew rate problems, etc.
However if the EMI is at a much higher frequency than what the amplifier can process, then it rectified and detected by semiconductor junctions and turned into a noise signal that looks like the envelope of the RF signal. That's why you hear the famous cellphone beeps in the loudspeaker before the phone rings, if the amp does not have EMI countermeasures.
The circuit you show works differently depending on frequency. I don't want to type &quot;at a higher frequency&quot; at the beginning of each line, o, from low to high frequency:

the caps don't do anything.

C3 which has higher value than C1 and C2 begins to filter differential HF noise

C1 and C2 begin to act, and their mismatch does convert some of the common mode into differential mode, but that is neutralized by C3 which has much higher value

Then finally at very high frequency, C1 and C2 short the RF to ground.


So the key is that C3 has higher capacitance than C1 and C2, so when C1 and C2 mismatch converts CM noise into DM noise, it is removed by C3.
EMI Rejection Ratio of Operational Amplifiers
AN-1698 A Specification for EMI Hardened Operational Amplifiers
There is another circuit which is very clever, from THAT1200 series of differential receivers:

Here C1 and C2 play the same role as your C3 cap, they filter differential noise. Their common node is connected to ground via one cap, C3, and this cap is bootstrapped, at low frequency the chip drives it via R3 and Cb so the current that flows through C3 does not come from C1 and C2, it comes from the driver instead. This means the common node between C1 and C2 is always kept at the common mode voltage, which means mismatch between C1 and C2 does not cause common mode to differential conversion, because no common mode current flows in C1 and C2.