... claims of searching the roles for Mexican names to target for immigration raids ...
I've never resided in Texas nor taken a Texas History course, but I know that, just like California, are are people with Hispanics living there whose ancestors were in the state when Texas (and California) were Spanish colonies and what is now the US was a collection of British colonies. Or whose ancestors came into the US legally. Or are themselves legal immigrants. Plus or minus a hypothetical few DEI/AA-hires, I'm sure that ICE and CBP people know this, too.
Sadly, the states most likely to have significant numbers of ineligible, multi-registered, moved out of state, and deceased voters on their rolls are the ones resisting providing the data.