Why would showing ID supress legal voters?
one recent example are Native Americans in North Dakota
The voter ID law in that states requires that their ID have a street address
Apparently many Native Americans don't have a permanent address and use PO Box on their ID
So they have a perfectly valid ID but it can't be used to vote
You can find many other examples where these laws are DESIGNED suppress or deter legitimate and legal voters from voting
Luckily it turns out they are not nearly as effective at voter suppression as Republican had hoped
BTW - you can find many legal challenges where various voter ID laws were overturned and the judge concluded the intent was suppression