Question: Barriers and resistance
Confirmation bias, special pleadings, dogmatic belief systems, red herrings, and hasty generalizations. In logic, fallacies could apply to any paralogical (fallacious) reasoning that resists or restricts the discovery of truth. No, atheism is not a barrier or restrictor of logic. This is a gib appeal to nonsense.
Obviously, neither atheism (science) nor theism (faith) are barriers or resistors to the truth per se - since it is possible for either one to arrive at its opposite conclusion. At least we have anecdotal evidence for both sides. (Francis Collins to Theism, or Darwin to atheism (arguably)
Atheists pretty much reject faith (theology) as a valid epistemology since it relies upon supernatural pleadings that contradict the laws of physics. Atheists simply reiterate: extraordinary claims require extraordinary evidence. (Sagan) A perfectly logical clam.
Theism relies upon four basic pillars: Cosmological, Moral, Teleological and theological. All of which have been thoroughly refuted. Nevertheless, it is possible to study or even argue these pillars and come to reject them as well. So, not necessarily a barrier in itself.
As for which is The Absolute Truth - we may never know. As a logician, I am more inclined to agree with Dr. Andrew Borstein who writes so eloquently, “the tragedy of theology in its distilled essence: The employment of high-powered human intellect, of genius, of profoundly rigorous logical deduction—studying nothing.”