This is demonstratively false.
Data indicates that states led by Republican governments generally have higher per capita violent crime rates compared to Democratic-led states. Analyses of crime data from recent years show that many of the states with the highest violent crime rates lean Republican, whilst states with the lowest rates tend to lean Democratic.
For instance, in 2020, nine out of the ten states with the highest violent crime rates were Republican-led, whereas eight out of ten states with the lowest rates leaned Democratic.
Homicide rates have also generally been higher in Republican-leaning states over the past two decades, partly attributed to factors like higher poverty, greater gun ownership, and lower investment in social services in those regions. I would also say that the increasingly violent and bigoted rhetoric from Republican leaders has contributed to that trend.
Currently, the majority of the states in the top 25 for per capita violent crime, per FBI statistics, are Republican-led.