Color-independence conjecture for surface cluster structures

Let $S_{g,\sigma}$ be a marked bordered surface whose marked points carry colors, and let $\mathcal{A}(S_{g,\sigma})$ denote its associated cluster algebra. Choose any subset of boundary components.

Color-independence conjecture. Changing all colors of marked points on any subset of boundary components does not change the cluster type of $\mathcal{A}(S_{g,\sigma})$.

The claim predicts that the cluster type is independent of these boundary color choices. The supplied text gives no resolution status.