Seems to me there could be a common pattern:

If a political group X, identified as A in {"left", "right"}, becomes very powerful in some era, the following things happen:

• people see X as a prototype of A;
• other A groups are seen like less successful variations of X; if that is impossible, the cognitive dissonance will be solved by reclassifying the incompatible group as non-A;
• after a while X (and therefore A) becomes the default position for people who don't think too much about politics.

Later, when the political group X loses some power:

• simple people still identify as X (A), which is reinforced by seeing the past with rose-colored glasses;
• new opinions are automatically classified as non-A, because they don't pattern-match X;
• therefore smart people begin to identify as non-A, to signal intellectual superiority and independent thinking.

In USA, X = Republican / religious right, and A = "right". In Eastern Europe, X = Communist, and A = "left".

This is very simplified, but it explains why sometimes the same person could self-identify as "left wing" in USA (to express their incompatibility with the religious right), and as "right wing" in Eastern Europe (to express their incompatibility with the communists). On the other hand, people mostly compatible with the religious right or with the communists can self-identify the same in both places.

In Eastern Europe the distinction between "support the traditional model" and "support change" is rather confused, because it is not clear whether the traditional refers to the era before the fall of communism, or to era even before the communists. In some sense, both religious right and communists are literally the conservative parties here.