i think one can’t really infer inconsistencies from survey data all that often (as in “n% of people think X, and m% of people think y, but those are incompatible”). if n% of people say X (m% say Y), and 100-n% of people say ¬X (and 100-m% say ¬Y), and X and Y are incompatible, then the groups that say X and Y only must overlap with (X-50)+(Y-50) percent, which is often not that much.