Hallelujah, brother! And it's about time, too.
Which party you chose will be made public, according this excerpt from a story by Julie Mack here:
Within 71 days after the election, the Secretary of State will have available an electronic list of voters who cast a ballot and which party they choose. That list will be available to the public for 22 months.
The change was recommended in August by the Michigan Republican Party, to reduce the number of Democrats participating in the Republican primary. "We should have a process by which Republicans choose the Republican nominee for president," one official said.