Does the Municipal Utility Customer Privacy Law prohibit the use of postcard billing?

No.  Although it was initially unclear whether postcard billing violated the prohibition on release of customer information under Act 25, sec. 196.137(5) now clearly provides that a municipal utility that sends a billing statement to a customer on a postcard does NOT violate the prohibition against releasing customer information except as specifically authorized.  Section 196.37(5) was created by 2013 Wis. Act 134 and took effect February 28, 2014.