Conformist social learning can have a pronounced impact on the cultural evolution of human societies, and it can shape both the genetic and cultural evolution of human social behavior more broadly. Conformist social learning is beneficial when the social learner and the demonstrators from whom she learns are similar in the sense that the same behavior is optimal for both. Otherwise, the social learner's optimum is likely to be rare among demonstrators, and conformity is costly. The trade-off between these two situations has figured prominently in the longstanding debate about the evolution of conformity, but the importance of the trade-off can depend critically on the flexibility of one's social learning strategy. We developed a gene-culture coevolutionary model that allows cognition to encode and process information about the similarity between naive learners and experienced demonstrators. Facultative social learning strategies that condition on perceived similarity evolve under certain circumstances. When this happens, facultative adjustments are often asymmetric. Asymmetric adjustments mean that the tendency to follow the majority when learners perceive demonstrators as similar is stronger than the tendency to follow the minority when learners perceive demonstrators as different. In an associated incentivized experiment, we found that social learners adjusted how they used social information based on perceived similarity, but adjustments were symmetric. The symmetry of adjustments completely eliminated the commonly assumed trade-off between cases in which learners and demonstrators share an optimum versus cases in which they do not. In a second experiment that maximized the potential for social learners to follow their preferred strategies, a few social learners exhibited an inclination to follow the majority. Most, however, did not respond systematically to social information. Additionally, in the complete absence of information about their similarity to demonstrators, social learners were unwilling to make assumptions about whether they shared an optimum with demonstrators. Instead, social learners simply ignored social information even though this was the only information available. Our results suggest that social cognition equips people to use conformity in a discriminating fashion that moderates the evolutionary trade-offs that would occur if conformist social learning was rigidly applied.