Quantum mechanics is extremely counter-intuitive where contradiction is both true and real. Something can exist as both particle and wave, which doesn't make sense but is true. A particle can exist everywhere at once, but more so in one place than another. Schrodinger's cat is both alive and dead at the same time. These things are contradictory and nonsensical but absolutely true and verified by the chair you're sitting in and the screen your looking at. Logic, and reason, are merely descriptions rather than rules and have limits. Ultimately words aren't nearly as important as results. Rationalism falls to Empiricism.
If it is hypocritical to tolerate belief systems other than your own, then I say hypocrisy is a virtue rather than a vice. And isn't something to be shunned...if it yields the desired result. Maybe not by you personally, but by the human race. If consistency leads to something counter to the goal, then consistency is something to be taken with a grain of salt. Pragmatism at work.
The problem is your situation of why consistency is necessary in this particular instance holds no water. Saying "don't murder" and at the same time "Don't take away harmless people's rights" isn't going to lead to higher taxes or pedophiles. Your means of achieving consistency by attempting to disprove all other religions and making a single interpretation of the bible as correct leads to a world wide holocaust. So why is consistency preferable in this case to paradox?
Your Obama analogy is an attempt to make one peg fit all holes. If contradiction is bad here, it must be bad in all instances. If consistency would be good in this instance it must always be good.
Contradiction and paradox are both day to day occurrence and a necessity for the existence of society, life, and apparently the universe.

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