Hi,
Yes, it is a filter.
All is stable when there is DC load. With and without the RC.
But without RC ... when there is pulsed load current it might cause ringing.
It's because
* "pulses" consist of (a couple of) high frequency
* the OPAMP open loop gain decreases with higher frequency
* thus the OPAMP output becomes high impedance with higher frequency
* and thus - every pulse causes ringing in the output signal
Now the RC (output) becomes low impedance at higher frequencies. This stabilizes the output voltage and reduces the negative peak caused by the pulse.
On the other side the Opamp now has more time to compensate for the pulse current.
And the R reduces ringing.
The Opamp feedback connected at the C helps to avoid DC voltage errors caused by the load current (voltage drop across R)
The problem may be...
The RC causes delay, it adds another pole in the Opamp feedback. This reduces phase margin for the feedbacked circuit.
In worst case the whole circuit starts oscillating.
--> with the RC you need to choose a suitable Opamp.
Klaus