Reagan was no liberal. He was Governor of California during the free speech movement, and aggressively moved to use force (national guard; and he encouraged local officials to use the police) to suppress protests (including peaceful protests) and colluded with the FBI to spy on pro-free-speech individuals and anyone who was trying to find a moderate position.

There is no perspective where spying on Americans because they are saying the wrong things, and using force against them to prevent them from gaining greater freedom to speak out, is "liberal". It's completely antithetical to liberal values.

Reagan, as an actor, may have occasionally been able to play the role of the classical conservative liberal, but that's about it.

William F. Buckley was arguably a classical conservative liberal.