The complex nature of microbiome data has made the differential abundance analysis challenging. Microbiome abundance counts are often skewed to the right and heteroscedastic (also known as overdispersion), potentially leading to incorrect inferences if not properly addressed. In this paper, we propose a simple yet effective framework to tackle the challenges by integrating Poisson (log-linear) regression with standard error estimation through the Bootstrap method and Sandwich robust estimation. Such standard error estimates are accurate and yield satisfactory inference even if the distributional assumption or the variance structure is incorrect. Our approach is validated through extensive simulation studies, demonstrating its effectiveness in addressing overdispersion and improving inference accuracy. Additionally, we apply our approach to two real datasets collected from the human gut and vagina, respectively, demonstrating the wide applicability of our methods. The results highlight the efficacy of our covariance estimators in addressing the challenges of microbiome data analysis. The corresponding software implementation is publicly available at https://github.com/yimshi/robustestimates.