This is a major reason why Thune and Republican Senators are not pushing the SAVE act very hard in Congress. -- because the SAVE act could hurt Republican voters more than Democratic voters.
20 years ago, most educated white people voted for the Republican Party. However, those days are long gone. Most educated white people now vote for the Democratic Party because the MAGA Republican Party has simply become too stupid, mean, and racist for the average educated white voter.
I promise you that the average white uneducated MAGA hillbilly living in West Virginia or Alabama does not have their birth certificate or marriage certificate and they are not going to jump through extra hoops to get it. However, educated white voters (mostly Democrats) will just through those extra bureaucratic hoops.