My guess is that the receiver clock glitches in some way when the MSI auto calibration runs, but it never showed up on the transmitter (and the device on the other side of the connection has never had a reception issue).

I ended up disabling the auto cal feature during a UART reception and then turning it back on when the reception is done.

SPI is definitely better as far as clocking, but MCU support as a SPI receiver is sometimes a lot less convenient to deal with.

A lot of UARTs have a synchronous mode which adds a dedicated clock signal - I've used that before out to a couple MHz.

In this application though, I'm only running 1 MHz so I really didn't think I should need a separate clock (and, it turns out, still don't).