The degraded performance and group unfairness caused by confounding sensitive attributes in rumor detection remains relatively unexplored. To address this, we propose a two-step framework. Initially, it identifies confounding sensitive attributes that limit rumor detection performance and cause unfairness across groups. Subsequently, we aim to learn equally informative representations through invariant learning. Our method considers diverse sets of groups without sensitive attribute annotations. Experiments show our method easily integrates with existing rumor detectors, significantly improving both their detection performance and fairness.