And yet I am required to show ID to buy alcohol, fly on a plane, purchase a firearm, etc. Granted, only purchasing a firearm is a right, but why does that require ID but voting doesn't? Politicians tend to kill significantly more people than your average citizen.
Another interesting place(s) that you have to show ID where, while you don't have a God given right to enter, you have a right as a citizen: Most government buildings serving the public.
If I want to interact with the government bureaucracy that my tax dollars pay for, I have to show ID. Either at the front door for security, and/or at whichever office I'm doing business with inside. How is that not the same burdensome discrimination against the poor and whatever other groups?
If I don't have to prove my identity to vote, I don't have to prove my identity to interact with the government I pay for in other ways either.
Also, kind of an analogy -- I went fishing in a National Park last week and showed my annual interagency pass at the gate. They made me show my drivers license as well to prove that the interagency pass was mine. So I had to prove that I was me to get into a National Park, but I don't have to prove I'm me to get my ballot and vote.