"No, I'm asserting they were eligible voters, and now some of them will lose that eligibility unless they jump through a new hoop. (And not because of anything they did, such as commit a felony.)"
It's a hoop they've already jumped through. Your challenge it to convince me why it was OK to force them to show an ID when they drove a car, or bought a gun, or opened a bank account, or installed a phone line; but to force them to show one now is just a bridge too far.
"For others, they have to jump through a new hoop, one that you favor putting between them and the voting booth."
Actually, there are many hoops. they have to get out of bed. They have to drive to the polling location. These are also required to vote. Are these just additional forms of disenfranchisement? After all, if I don't own a car, how could I get to the polling location?