60 years ago would be 1953. Nobody back then would consider a party whose core principle is keeping the top tax rate at 35%.
Cool story bro. http://library.cqpress.com/cqresearcher/document.php?id=cqresrre1947040900#.UedSSxaTM20
Anyway, rightly or wrongly, people in the year 1953 are not exactly going to cotton to a party with the modern-day Democrats' views on gay rights, abortion, school prayer, racial issues, etc., and propensity for denouncing anyone who disagrees with those views as a bigot.
I see both of your points.
Anyway, obviously American politics is more conservative these days, relative to the corresponding time period (since comparing the conservatism of today to the past in absolute terms is rather silly...the past is usually by definition, more "conservative.")
