We present an experimental investigation of supercontinuum generation in potassium gadolinium tungstate (KGW) and yttrium vanadate (YVO) crystals pumped with 210 fs, 1030 nm pulses from an amplified Yb:KGW laser operating at 2 MHz repetition rate. We demonstrate that compared to commonly used sapphire and YAG, these materials possess considerably lower supercontinuum generation thresholds, produce remarkable red-shifted spectral broadenings (up to 1700 nm in YVO and up to 1900 nm in KGW) and exhibit less bulk heating due to energy deposition during filamentation process. Moreover, durable damage-free performance was observed without any translation of the sample, suggesting that KGW and YVO are excellent nonlinear materials for high repetition rate supercontinuum generation in the near and short-wave infrared spectral range.