Only US citizens can vote in US federal elections. That is a federal restriction which is not impacted by this.
This is adding an additional requirement to show proof of citizenship before even being allowed to cast a vote.
According to this, people cannot vote for local or state level issues if they do not show a passport, birth certificate, certificate of citizenship, or other such document. Pretty sure drivers licenses and state issues IDs are not proof of citizenship, so a lot of people are probably going to be surprised when they show up and are not allowed to vote for governor, state legislature, etc because they don't have the right documentation.
This makes voting more restrictive, not less.