Ultra-thin material plus dimensional instability: What could possibly go wrong?

Flat or folded, flex circuit designs provide superior impedance performance across a wide spectrum of signal speeds.

Question: Will impedance change when the flex portion of a rigid-flex is bent into place during assembly?

The short answer is no.

When a circuit is bent, the distance from a single-ended or differential pair to the reference planes remains constant, as does the distance between traces in a pair. There is no compression of the dielectric or movement of signal lines. As a result, the impedance remains constant as well. The performance as modeled in the flat condition will continue when bent.