Training language models and examining their linguistic behaviors have been a common protocol in computational linguistics for studying linguistic phenomena and modeling human language processing. However, work in this area is often limited to proof-of-concept demonstrations with arbitrary model configurations, without considering hyperparameter sensitivity, an important source of variation in model performance. In this work, we replicate three prior studies (Chang and Bergen, 2022; Hu et al., 2020b; Kuribayashi et al., 2024) with hyperparameters varied within a practical range, and show that modest hyperparameter changes can alter some qualitative conclusions about models’ linguistic abilities and even reverse the ranking of model performance. Our results highlight the risk that prior work may have reflected optimization artifacts rather than the genuine inductive biases of model classes, and that hyperparameter sensitivity should receive more attention as a factor that can meaningfully influence model behavior. We suggest future work to report the variation of performance across the configuration space to enhance the reliability and generalizability of conclusions. Code: https://github.com/compling-wat/tune-linguistic-lms.