Just an update, I went ahead and pulled off the t-shaped molding between the doors. It pulled right off through the brads by hand, then I pulled the brads out of the RHS door carefully with some side cutters.
The upside is the doors no longer rub against each other, and now we can open only the left hand door. This is convenient for grabbing something out of the medicine cabinet, brushing teeth, etc.
The downside is there's now a gap between the doors that somewhat reduces privacy. Not an issue for us, but that's the only downside I could think of.