How should I repair small tears in the kraft paper insulation caused while running a new water line?
You're right that your bathroom will have a lot of moisture in it, but if that much gets through to your insulation you're not ventilating enough. Make sure you run your bath fan regularly and for long enough, and don't overthink the repair. Use any tape that will bond well to the craft paper, except not masking or duct tape. Neither have adhesives that are suitable for the long-term.