Recent advances in Large Language Models (LLMs) have upgraded them from sophisticated text generators to autonomous agents capable of cooperation and tool use in multi-agent systems (MAS). However, it remains unclear how disagreements shape collective decision-making. In this paper, we revisit the role of disagreement and argue that general, partially overlapping disagreements prevent premature consensus and expand the explored solution space, while disagreements on task-critical steps can derail collaboration depending on the topology of solution paths. We investigate two collaborative settings with distinct path structures: collaborative reasoning (CounterFact, MQuAKE-cf), which typically follows a single evidential chain, whereas collaborative programming (HumanEval, GAIA) often adopts multiple valid implementations. Disagreements are instantiated as general heterogeneity among agents and as task-critical counterfactual knowledge edits injected into context or parameters. Experiments reveal that general disagreements consistently improve success by encouraging complementary exploration. By contrast, task-critical disagreements substantially reduce success on single-path reasoning, yet have a limited impact on programming, where agents can choose alternative solutions. Trace analyses show that MAS frequently bypasses the edited facts in programming but rarely does so in reasoning, revealing an emergent self-repair capability that depends on solution-path rather than scale alone. Our code is available at https://github.com/wbw625/MultiAgentRobustness.

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