Reagan was a bit before my time as an adult, so I don't have a solid opinion of the emotional content of his speeches. But I don't think it was a bunch of everything about the US is broken and wrong, and we need to tear it down. I feel like the cognitive dissonance was much more narrowly scoped to those specific social issues you're talking about.
Also note that conservatism is necessarily a product of the times. A position that was considered conservative in the 1980's is likely not conservative a generation and a half later.
If you want a really jarring example of this, watch Bush (Sr.) and Reagan debate immigration during the 1980 primaries. https://www.youtube.com/watch?v=YsmgPp_nlok
They sound like Democrats today. (And that's in the primaries, where people tend to be more party-line!)