We appear to have misunderstood each other, having something different in mind by words like "skepticism" and "reject." I agree Con(ZF) entails Con(ZFC), and that every educated mathematician knows it. Beyond that I don't have a good handle on what you're saying, or even whether you disagree with Yudkowsky, or me. Are you saying that mathematicians pay lip service to constructivism, but ignore it in their work? Are you additionally saying that there is something false about constructivist ideas?

It tends to irritate me when people get something wrong which they could easily have gotten right by using a standard human heuristic (such as the "status heuristic", noticing what the prestigious position is).

That doesn't sound like such a great heuristic to me...