Drought severity is commonly assessed using indices that measure water deficits against a historical baseline of hydroclimate observations. However, the utility of drought classification, which often depends on a fixed reference period, is uncertain as the climate continues to change rapidly. In our study, we evaluate several widely used drought indices—including the Standardized Precipitation Index (SPI), the Standardized Precipitation-Evaporation Index (SPEI), the Evaporative Demand Drought Index (EDDI), and the Soil Moisture Drought Index (SMDI)—using ERA5-Land reanalysis across the western United States from 1950 to 2023. We assess the sensitivity of each index to climate non-stationarity by applying bootstrap resampling to historical reference periods, which allows us to quantify how reference-period dependent variability affects drought severity assessments. Our findings show that indices incorporating evaporative demand estimates, such as SPEI and EDDI, indicate that the most extreme historical droughts are up to 24% less severe when a modern reference period (1991-2020) is used, compared to using the entire record. Additionally, we demonstrate that decadal variations in precipitation can skew SPI and SMDI drought severity assessments by –0.3 to +0.5 standard deviations, introducing significant uncertainty in classifying any single drought event. We also examine the uneven impact of non-stationarity on the variability of wet and dry extremes across the region to better understand each index's utility across different western US hydroclimates. Our study aims to enhance the quality of drought information and highlight the uncertainties inherent in popular drought classification methods.