The Supreme Court, in a 6-3 decision, ruled that it's Constitutional. End of story, for all intents and purposes.
If you support voter ID, then you support that idea that only people eligible to vote CAN vote. If you don't support voter ID, then you support the idea that people who are ineligible to vote CAN vote.
It's not about should, it's about CAN.
Illegal voters disenfranchise legal voters!