An interesting question, and not an easy one to answer in the way I could be sure you understood the same thing what I meant.

My original thought when composing the comment was that it never occurred to me that "he doesn't have a PhD so his opinion is less worth", and I would never use the fact that he doesn't have a PhD, neither in an assumed debate with him nor for any self-assurance. This means that even if I answered with a "clear yes" to your question, it still wouldn't mean that it was the cause of the rejection.

Loss of credit because he doesn't have a PhD does not necessarily equal the gain of credit because he does have a PhD. Yes, I realize that this is the most attackable sentence in my answer.

The disagreements are more centered on personal opinion, morality, philosophical interpretation, opinion about culture and/or religion, and in part on interpreting history. So, mostly soft sciences. This means that there would be no relevant PhD in these cases (a PhD in a philosophical field wouldn't matter to me as a deciding factor)

On the other hand, if it was a scientific field, then I might unconsciously have given him a little higher probability of being right if he did have a PhD in the field, but this would be dwarfed by the much larger probability gain caused by him actually working in the relevant field, PhD or not. As of yet I don't have any really opposite views about any of his scientific views. Maybe I hold some possible future events a little more or less probable, or am unsure in things he is very sure about, but the conclusion is: I don't have scientific disagreements with him as of yet.

About whether this type of rejection is common: if we take my explanation at the beginning of this answer, then I guess it is uncommon to reject him in that way (and his article might lean a tiny little bit in the direction of a strawman argument: "they only disagree because they think it's important that I don't have a PhD, so this means they just don't have better excuses"). If we take your definition, then I agree that it might be higher.