Reagan was a Democrat until he became a Republican.
Convenient, isn't it.
Reagan became a republican because as a conservative the democratic party no longer offered a home for him. His principles were with the republican party, and he helped push it further to the right.
Rudy became a republican because it was a way to get jobs from them. His principles are with the democratic party, and the only thing he would do to the republican party is push it further to the LEFT.