Why are voter lists public?
The “elections clause,” found in Article I, Section 4 of the Constitution, grants both Congress and individual states the power “to enact a complete code for . . . elections, including rules concerning public notices, voter registration, voter protection, fraud prevention, vote counting, and determination of election results.” States determine the “Times, Places, and Manner” for conducting elections, and this broad authority allows states to control nearly every aspect of the electoral process. Congress typically defers to the states on electoral matters like voter registration.
With that, decisions about what voter information is made available are made at the state level, and each state has access requirements for their voter lists. This National Conference of State Legislatures (NCSL) table describes which pieces of voter information are/are not made public, who may access voter lists in each state, and the state regulations governing the process.
Vote Forward notes that voter rolls are public in the overview for voters who receive letters and offers information on the possibility for some voters in certain states to make their voter record or part of their voter record private.
NCSL has additional resources on its website if you are interested in reading more about this topic, including this statement from the U.S. Elections Assistance Commission.