This paper addresses the problem of optimizing the allocation of labeling resources for semi-supervised belief representation learning in social networks. The objective is to strategically identify valuable messages on social media graphs that are worth labeling within a constrained budget, ultimately maximizing the task's performance. Despite the progress in unsupervised or semi-supervised methods in advancing belief and ideology representation learning on social networks and the remarkable efficacy of graph learning techniques, the availability of high-quality curated labeled social data can greatly benefit and further improve performances. Consequently, allocating labeling efforts is a critical research problem in scenarios where labeling resources are limited. This paper proposes a graph data augmentation-inspired perturbation-based active learning strategy (PerbALGraph) that progressively selects messages for labeling according to an automatic estimator, obviating human guidance. This estimator is based on the principle that messages in the network that exhibit heightened sensitivity to structural features of the observational data indicate landmark quality that significantly influences semi-supervision processes. We design the estimator to be the prediction variance under a set of designed graph perturbations, which is model-agnostic and application-independent. Extensive experiment results demonstrate the effectiveness of the proposed strategy for belief representation learning tasks.