Social tipping can accelerate beneficial changes in behaviour in diverse domains from equality and social justice to climate change. Theoretical work, however, shows that group identities or heterogeneous preference can undermine tipping in ways policy makers do not anticipate and alter which subset of a population should be targeted by policymakers aiming to accelerate behavioral change through circumscribed interventions. To examine this, we ran virtual lab experiments in which participants faced incentives to coordinate their choices. Once participants had established a coordination norm, an intervention created pressure to tip to a new norm. In a group identity study, we used neutral labels for choices in the control group and partisan political image labels in the identity treatment group. This simple payoff-irrelevant relabelling generated extreme differences. Control groups developed norms slowly before intervention but transitioned to new norms rapidly after intervention. Identity groups developed norms rapidly before intervention but persisted in a state of costly disagreement after intervention. Tipping was powerful but fragile. It supported striking cultural changes when choices and identity were unlinked, but even a trivial link destroyed tipping entirely. In subsequent work, we use a similar paradigm to investigate how heterogeneous preferences interact with the magnitude and targeting of tipping interventions to shape social tipping dynamics. We find that pre-intervention heterogeneity significantly moderates the efficacy of tipping interventions. The results of these two studies suggest that social tipping interventions are not guaranteed to drive widespread behavioral change and depend critically on mundane features of societies.