Perhaps you are not aware that the Republican Party has a platform stating its principles and beliefs.I'm very well aware of it. In fact I have a post in this very thread that specifically mentions the platform. I believe it went like this: People should consider that it's not a matter of voting for someone with talking points to their liking. The trick is getting your talking points into the Republican National Platform, then putting forth a Republican that is electable.
Now using Rudi as the most extreme example, it would be complete folly to believe that if he were elected President, he would support the DNC platform rather than the RNC platform. All presidents are beholding to those that elected them. People that tirelessly pimped their agenda for them, raised hundreds of millions of dollars for them. People that went to friends and business associates begging for money in the name of their favorite candidate or 527.
Johnson couldn't stand any of the Kennedys, yet he kept JFK's entire cabinet for most of his entire term. He pushed for passage of Kennedy's tax cut and civil rights bill and declared a "War on Poverty." Basically the money behind the Democrats in 1960 said "We have power, we have money, here's our platform and JFK is going to sell it for us." Changing presidents didn't change the platform.
Unless George Soros starts funding the RNC, Rudi Giuliani isn't going to drive any liberal campaigns into law.
A liberal who registers Republican is, literally, a Republican, just not a conservative.