Adding supplementary variables to clr-based PCA

Hi all,
I regularly work with compositional data, for which it is recommended to apply a clr-transformation before making a PCA. This is fine. Now, to explain the variance seen in the PCA, I need to project supplementay/explanatory variables that do not affect the shape of the PCA. Should the explanatory variables (for the same samples) also be transformed in clr?
My main dataset is geochemistry, and the supplementary variables are mineralogy (so also compositional data).
Thank you!