this statement suffers from LOGIC paralysis.
Almost certainly, if you say supporters of X are almost certainly in favor of Y , then you are looking for a "common cause" and not for cause and effect between the X and Y.
The Left-Right designation is deficient too since Conservatism (if you are Conservative by intellectual conviction) is the absence of ideology, I think it was the great Conservative thinker Russell Kirk who said that Conservatives and LIbertarians have only ONE thing in common, fear of highly-centralized power. Yet on your view of things they would both be on the Right. As if one could really find commonality in William F Buckley, Ayn Rand, and Hitler !!
Bottom Line: That there is a Left-Right divide is purely a figment of the Left :)