There isn't any consent involved.  The publication of any personal information found in the public record is uncontrolled.  By it's very nature and name, the public record is public.  It is the price we pay for living in a free and open society with public records that can be accessed by one and all.
     The Media that the record is published on, is relevant, but only so far.  For the sake of philosophical argument, lets throw economics (of what it would cost) and physics (of how much space it would take up) out the window for the moment.  Would you object to giving every person in the United States a paper copy of every public index and document in one county in Texas?  They would have access to the public record at their fingertips, and all the personal information contained within, they would simply have to physically page through every record.
     Access to the records is different than the availability of the records in a digital format.  As long as I can walk into the county courthouse, pick up a pen, and write a matrix of names, Address, SSN, Bank Accounts, Etc... on a sheet of paper and then publish it on the front page of USA Today nationwide, then it really doesn't matter if the records are online, digital images, or paper copies, as I can still acquire and publish the information.