Instead of blind-faith in religious tenants, my world-view currently accommodates two traditionally exclusive systems of belief: religion and science.

In other words, it seems you meant "doublethink" in the collective sense based on traditional sentiment, rather than in the actual sense of a logical contradiction between any one specific religious tenet A and any one specific scientific theory B. If there are no actual contradictions, "doublethink" was just an (unfortunate) turn of phrase and there is nothing to be reconciled.