I'm a T2/no meds. I use whey protein post workout. Whey is a fast digesting protein and it will raise my BG. Bodybuilders suggest this type of protein post workout with a carb (often fast digesting) because they are looking to raise insulin levels and get the whey protein into the system quickly. I lift in the morning and have dawn phenomenon so, I drink a low carb whey shake post workout and don't bother with the insulin spike since nature has done that for me. Some may have a small amount of simple carbs like 6oz grape juice. I would think covering your carbs from the shake with insulin is just fine. Admittedly, I'm not an expert. If I have a protein shake before bed or just want something slow digesting (maybe to replace a meal) you may want casein or a mix of different proteins or even egg (moderate digesting protein). I add a little fat to my slower digesting proteins (grass fed cream/pure coconut milk) to slow it down even more since most protein powders are also low fat.
As far as kidneys go. If you have no previous condition you should be fine. I personally wouldn't chug tons of protein and I would make sure that you drink enough fluids. I had a kidney stone (calcium) and asked my specialist (well respected in my area)if I should adjust my diet. He said no since it was my first stone, but to make sure I get my fluids. Of course, speak to your physician regarding your own medical history. :)