Nah, in principle this is something that could be quantified. But the question we would want to ask is "do people who self-identify as theists or atheists contribute disproportionately to harmful stereotypes?" In other words, you would look at if the quantity of stereotypes being generated by a group relative to the population of the group. Say we've got 100 stereotypes, and are sampling 100 people, 10 of whom are atheists and 90 of whom are theists. All else being equal, we'd expect 90 of the stereotypes to be coming from thesis, and 10 from atheists. If instead it's something like 70 coming from theists and 30 from atheists, we'd have evidence of your point.
Granted, while I see this as possible in principle, I don't see how it would be done in practice in a manner that would be methodologically sound. Nor do I understand what the point such a study would be, other than to paint theists or atheists as "the bad guys" for being more guilty of using harmful stereotypes. I don't think dividing people into "theist vs atheist" is at all useful on the whole - certainly not with combating something as pervasive as stereotyping. It's "us vs them" thinking that helps produce stereotypes in the first place.