While existing social bot detectors perform well on benchmarks, their robustness across diverse real-world scenarios remains limited due to unclear ground truth and varied misleading cues. In particular, the impact of shortcut learning, where models rely on spurious correlations instead of capturing causal task-relevant features, has received limited attention. To address this gap, we conduct an in-depth study to assess how detectors are influenced by potential shortcuts based on textual features, which are most susceptible to manipulation by social bots. We design a series of shortcut scenarios by constructing spurious associations between user labels and superficial textual cues to evaluate model robustness. Results show that shifts in irrelevant feature distributions significantly degrade social bot detector performance, with an average relative accuracy drop of 32\% in the baseline models. To tackle this challenge, we propose mitigation strategies based on large language models, leveraging counterfactual data augmentation. These methods mitigate the problem from data and model perspectives across three levels, including data distribution at both the individual user text and overall dataset levels, as well as the model's ability to extract causal information. Our strategies achieve an average relative performance improvement of 56\% under shortcut scenarios.