Agricultural waste ashes represent a promising source of supplementary cementitious material (SCM); however, they must be washed (with water or acids) or co-processed with calcium-rich slags to mitigate deleterious reactions. Knowledge gaps remain regarding their fire performance and the evolution of pore-solution pH—both critical parameters for long-term durability. This study evaluated mortars incorporating 10 wt% rice husk ash (RHA), considering three treatment conditions: untreated (U), water-washed (W), and acetic-acid-washed (AA). After 28 days of curing, physical–mechanical properties and pore solution pH were determined. Additionally, selected specimens were subjected to a thermal shock at 500 °C for 1 h to assess residual strength. The ANOVA analysis revealed statistically significant differences in the mechanical behavior of the mortars depending on the applied treatment. Under fire-unexposed conditions, the incorporation of water-washed RHA significantly increased compressive strength and reduced strain, an effect associated with lower water absorption by immersion, reduced open porosity, and higher bulk density. However, after exposure to 500 °C, all mortars experienced mechanical degradation, which was more pronounced in those with pretreated RHA (−52.4% strength and +132.9% strain in W). Mortars with untreated RHA exhibited greater thermal stability, attributed to their coarser porosity that facilitated vapor release. Moreover, all RHA-containing variants substantially reduced system alkalinity (pH ≈ 8), a condition favorable for use with vegetal reinforcements, although limiting for reinforced concrete exposed to chlorides.