To be at loggerheads is to be in conflict with someone, and in this sentence the men are in conflict with each other over political issues.
Context: "He was even surprised to learn the men were pretty good friends when they weren't in conflict with each other over political issues."
Hypothesis: He was even surprised to learn the men were pretty good friends when they weren't at loggerheads over political issues.
Based on the context, is the hypothesis true, false, or unknown?