Classification of cells in microscopy images is an essential step in the diagnostic workflows for various medical conditions. These diagnostic processes benefit from emerging deep learning solutions, which make them more accessible, reliable, and scalable. However, their extensive deployment is hindered by limited generalizability and high computational demands of such architectures. We address this issue by introducing a lightweight, general-purpose hierarchical classification model based on Neural Cellular Automata (NCA). Our approach utilizes NCA to extract features at multiple resolutions, combining the advantages of NCA-based methods with those of convolutional architectures. We evaluate our model on six microscopy datasets from different modalities and demonstrate that it consistently outperforms existing NCA-based approaches. With significantly fewer parameters than conventional deep learning methods, our model is suitable for deployment in resource-constrained areas, such as remote clinics with limited computational infrastructure or mobile devices with lower computational capacities. Our results highlight the potential of NCA-based models as an effective, lightweight alternative for image classification, addressing critical barriers to the equitable distribution of automated diagnostic tools.