Increasing number of deaf or hard-of-hearing individuals is a crucial problem since communication among and within the deaf population proves to be a challenge. Despite sign languages developing in various countries, there is still lack of formal implementation of programs supporting its needs, especially for the Filipino sign language (FSL). Recently, studies on FSL recognition explored deep networks. Current findings are promising but drawbacks on using deep networks still prevail. This includes low transparency, interpretability, need for big data, and high computational requirements. Hence, this article explores topological data analysis (TDA), an emerging field of study that harnesses techniques from computational topology, for this task. Specifically, we evaluate a TDA-inspired classifier called Persistent Homology Classification algorithm (PHCA) to classify static alphabet signed using FSL and compare its result with classical classifiers. Experiment is implemented on balanced and imbalanced datasets with multiple trials, and hyperparameters are tuned for a comprehensive comparison. Results show that PHCA and support vector machine (SVM) performed better than the other classifiers, having mean Accuracy of 99.45% and 99.31%, respectively. Further analysis shows that PHCA's performance is not significantly different from SVM, indicating that PHCA performed at par with the best performing classifier. Misclassification analysis shows that PHCA struggles to classify signs with similar gestures, common to FSL recognition. Regardless, outcomes provide evidence on the robustness and stability of PHCA against perturbations to data and noise. It can be concluded that PHCA can serve as an alternative for FSL recognition, offering opportunities for further research.