All believers and non-believers are acting in ignorance of free will; while consenting to believe/not believe the suggested -isms by the free will of another. If you find yourself within the conflict of reason (true vs false) you consented to fight about what a 3rd party suggested you to fight about aka control through division by suggestion.

In this case...believing vs not believing in left vs right represents consent to the suggested choice by the free will of another. No matter what you choose; the initial choice is always ignorance towards free will of choice (ones own).

Its intentional and they don't care.

That represents the maintenance of the conflict of reason after gaining consent to ignorance towards free will of choice. Reason represents division through suggestion, and to keep it going the few suggest contradiction to reason (to both sides), which represents control over both sides of all conflicts. This is called talmudic reasoning, out of the same talmud that teaches implication (if/then) over reason (true vs false).