OK, so the theory that whey protein shakes could increase strain on your kidneys is not all that ludicrous. There is after all some evidence to suggest that people with renal (kidney) problems may damage their kidneys due to hyperfiltration. Hyperfiltration refers to glomerular filtration, a process that draws solute (a substance mixed into a solution) such as amino acids (broken down protein) from fluid and back into the body. If an increased rate of filtration occurs due to elevated protein intake, then already weakened kidneys may suffer due to the increase in glomerular filtration rate.
The good news is that if you have normal functioning kidneys, and mercifully most people do, then the filtration process that occurs after the consumption of any protein (not just whey protein) is absolutely normal and poses no issue to the kidneys whatsoever. The glomerular filtration rate is adaptive, meaning it will NOT deteriorate as a result of increased protein intake.
So put your mind at rest, enjoy your protein shake and bask in those GAAAIIINNNNSSS!
NOTE: Intakes above your Reference Nutrient Intake (RNI) or Recommended Daily Intake (RDI) are not recommended in any instance.
Oldale, C. (2014). The Role of Protein in the Management of Malnutrition. Retrieved 23rd October, 2014, from http://www.nutrition2me.com/images/free-view-articles/free-downloads/cnfvol.4no.2_protein.pdf