Twelve states and D.C. allow illegal immigrants to acquire drivers licensees [0]. Washington State was the first one in the early 90s, but the list also includes the boarder states of California and New Mexico. I would imagine if a state will issue a drivers license then someone has to be selling insurance, otherwise the license is moot as their would be no legal way to drive.

[0] https://immigration.procon.org/view.resource.php?resourceID=...

Texas is not on that list though.