Yeah, most likely a little mildew. I would spray it down with some cleaner/disinfectant and move on. In my mind nothing to worry about and honestly I woudl more surprised if there were no mildew.

If you want to kill mold, spray it with vinegar. Bleach will kill mold on a non-porous surface, but vinegar will kill the parts that penetrate into a porous one.

From what I can infer, there appears to have been 15# felt installed over the paper-faced fiberglass batt insulation and stapled to the studs. I think what you're seeing is some deterioration in the paper and some transfer of asphalt from the 15# felt. The studs look dry and mold free.

Since you're redoing the shower, I suggest you remove and replace the insulation.