Suppose the opamps have a gain of zero. Then the outputs of the opamps will be essentially a short to ground. The circuit can then be analyzed as a purely passive network of resistors. Now imagine that the gain of the opamps is very small, perhaps 1/10. WIll the circuit latch up then? My analysis indicates that for sufficiently small opamp gains the circuit will be stable.I agree, of course.

But the question is not how an ideal opamp is to be defined, but:

Does it matter if we consider an opamp as ideal or real -as far as the stability of the DC operating point is concerned

This involves the loop gain only (and the stability criterion). In both cases, the loop gain > +1.

So the circuit will not assume a stable DC operating point.

This will not stabilize the circuit.

What do you calculate as the loop gain when the opamps have gains of .1 or 1?