OpAmp resistor to ground in feedback loop
R2 is not part of the feedback loop, it's just a load. Generally, it won't affect your stability, unless it draws enough current to reach the limit of your opamp output current. In that case you'll start losing gain and that might compromise stability, but it is hard to say what would happen and you'd have to experiment.

Let me just be clear that this sounds more like a mode of failure of the circuit than something you should plan out for during correct (intended) operation. If you're concerned about too much current then increase load resistance or pick a better opamp.