Afghan Allies Protection Act of 2021 This bill modifies a program providing special immigrant visas to eligible citizens or nationals of Afghanistan who assisted U.S. efforts there and addresses related issues. The bill extends the program through 2023 and increases the number of visas available. An individual may become eligible for a visa after assisting U.S. efforts in Afghanistan for one year, whereas currently some individuals must have served for two years. Furthermore, for an applicant qualifying for a visa by performing duties with a NATO mission in Afghanistan, the bill eliminates a requirement that the duties performed qualify as sensitive and trusted duties. The bill removes a requirement that the individual has experienced or is facing an ongoing serious threat due to their assistance to the United States or NATO. The Department of State or the Department of Homeland Security may postpone the program's medical examination requirement. An individual who received a postponement must undergo a medical exam within 90 days of admission into the United States. The bill also expands surviving family member benefits for the Afghanistan program (and a similar program for Iraq) to a surviving spouse or child of an individual who submitted an application to the Chief of Mission that would have been approved but for the individual's death. Currently, such survivor benefits only apply if the deceased individual's petition was approved.