My backsplash was installed first. The plugmold is sitting on top of it. If I removed the plugmold, there would be a perfectly intact backsplash remaining.

I am no expert but on the task lighting installation instructions for the angled plugmold they show a drawing with the backsplash directly below the bottom of the bar, not behind it. Therefore my answer is you can install the lighting first. I would protect it with frog tape while the tile work was being done.

See, you already have conflicting answers here, too!

My kitchen remodel is just finishing up (Thank goodness!) and
my plug mold was installed before the backsplash.

Abbey

There's no right or wrong way. We chose to do the BS first. That's because our plugmold doesn't run the full length of our wall. It would take more effort, time and waste to cut tiles around the plugmold. By doing the BS first and layering the plugmold over it, the whole thing looks more cohesive. Plus it gets the plugmold a little more forward (1/4"), making it just a little more accessible.

Our plug mold is connected to our cabinets, so would not matter.