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Cooperation in groups often requires individual members to make costly contributions that benefit the group as a whole. Prior research suggests that shared norms can help to support ingroup cooperation by prescribing common standards of how much to contribute. These common standards may be disrupted when groups undergo membership change, i.e., when members from outgroups enter the ingroup. When newcomers and incumbents have different notions about how much to contribute, a normative disagreement ensues that could undermine cooperation and the extent to which individuals identify with the group. In a laboratory experiment, we manipulate whether newcomers and incumbents disagree about how much to contribute in a public goods game with peer punishment. We examine whether normative disagreement between newcomers and incumbents affects newcomer-incumbent relations in terms of group identification, the emergence of a social norm, and costly punishment. The main goal is to test whether normative disagreement and the resulting newcomer-incumbent relations harm cooperation in terms of contributions to the common good. We find that normative disagreement between newcomers and incumbents negatively affects the emergence of a shared social norm and lowers feelings of group identification. Contrary to expectations, normative disagreement does not affect cooperation negatively. Instead, participants adjust their behavior to each other’s standards, using punishment for norm enforcement. This punishment is especially directed at low-contributing newcomers, leading them to conform to the incumbents’ higher contribution standards.