In general, the people against these kinds of things aren't against the simple extra check of something that's theoretically already true (registered to vote / ID at voting place, citizenship at banks, etc). They're against forcing people to provide arcane, asterisk-ridden (including married women! a large demographic!) documents.
If we just had a normal federal ID system like a normal country, where you just got one mailed to you when your kid was born just like their social security card manages to do, then this would all be much more fine. But noooo god forbid we be normal for once. Much better to keep using random bullshit in place of a national ID.