Coordination, Accountability, Research, and Equity for All Kidneys Act of 2021 or the CARE for All Kidneys Act of 2021 This bill requires multiple agencies to address kidney disease, with a focus on minority, rural, and other underserved populations that are disproportionately affected by the disease. First, the Department of Health and Human Services (HHS) must study patterns of care for kidney disease provided through certain health insurance providers. Second, HHS's Office of the Assistant Secretary for Health must (1) create a plan to address kidney disease, (2) develop a pilot program for best practices to diagnose and manage the disease, and (3) report annually on the impact of a Medicare model that encourages greater use of home dialysis and kidney transplants. Third, the National Institutes of Health must expand research on kidney disease. This includes research on the causes of lower rates of, and interventions to increase, kidney transplants among underserved populations. Fourth, the National Institute of Diabetes and Digestive and Kidney Diseases must conduct an awareness campaign and work with the Centers for Disease Control and Prevention (CDC) to evaluate data collection concerning kidney disease. Fifth, the CDC must award grants for public health interventions to reduce the burden of kidney disease and undertake activities to identify and address environmental and occupational causes of kidney disease. Last, the bill makes kidney disease specialists eligible for the National Health Service Corps (NHSC). The NHSC provides scholarships and student loan repayment awards to health care providers who agree to work in areas with shortages of primary care, mental health, and dental providers.