Hi @lca123,
The reason that you see the change is because you're re-doing rarefaction and so the distance matrix shifts slightly. (You can double check the alignment between the two matrices either using a mantel test or procrustes analysis if you still have both.)
You can flip the PCoA by going to the "axis" menu in Emperor and then selecting the "invert" checkbox for each axis you want ot flip. Since axes in PCoA are directionless, there is no consequence to flipping the axes.
If you want to prevent this in the future, you can skip the full core diveristy pipeline and re-generate the plots with new metadata using the emperor plugin. Here's an older post that discusses what's fully happening in core diversity analysis
Best,
Justine