You aren’t a conservative if you believe in conspiracy theories.
Before I defend this statement, I should say that as a general rule, I do not like statements that begin, “You aren’t a conservative if …”
It’s not that I always disagree with such assertions. For instance, “You’re not a conservative if you think the state should seize the means of production and usher in a new age of socialist economics” strikes me as not just defensible but self-evidently true—at least if you define “conservative” in the traditional Anglo-American sense. (The most committed Communists in the Soviet Politburo were routinely called “conservatives” because they were trying to conserve something very different from what American conservatives want to conserve.)
My objection is that when people say, “You aren’t conservative if …” they are usually confusing what is with what ought to be. Sure, conservatives ought to be (fill in the blank) pro-life, pro-gun, pro-free market, pro-this, or anti-that. But that doesn’t mean they all are. And if they disagree on this or that issue, they might simply be wrong. (Conservative is not synonymous with “correct.”) Or they might put more emphasis on different factors or concerns.