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Can a custodian refuse prior-year IRA/HSA deposit postmarked April 15?
The slips from your bank for your HSA account are for an account already established and thus the bank is willing to accept your deposits even if they arrive at the bank after the April 15 deadline, as long as the postmark  is April 15 or earlier. The account exists in the bank, they know who you are, and that the payment is received after April 15 is just due to the normal (or even abnormal) delays in postal delivery. For the new account that you tried to establish (with appropriate notarization and timely postmark etc), the credit union could not  have received the paperwork as of the close of business on April 15 (except in the very unlikely circumstance that a local letter deposited in the mailbox in the morning gets delivered the same day by USPS: don't extrapolate from stories of how mail was delivered in London in Victorian times). Ergo, you did not  have an HSA account in the credit union as of April 15, and they are perfectly correct in refusing to open an account with a April 15 date and put money into it for the previous tax year. To answer the question asked:  Are they allowed to ignore the postmark date? Yes, not only are they allowed to ignore the postmark date, the IRS insists that they ignore the postmark date. The credit union prefers to report only the truth: as of April 15, you had not established an HSA account as of April 15; to say otherwise would be making a false statement to the IRS.