As far as I can see, there is no non-blocking way to read the input from the uart0, if this uart is also used for REPL through dupterm.
In version 1.9 and before it is possible to use the UART.read() function for this, however since commit afd0701 the uart buffer is bypassed when UART 0 is used for REPL, so that UART.read() will never receive any data.
The input data is now directly put into the stdin buffer, which has (as far as I know) no function to check if any data is available.

The only workaround for this would be to disable dupterm for the uart0 while intending to read data. Yet, this is somewhat inconvenient, because then print() also won't output any data on the uart.

I think, the best option is to add a non-blocking read for stdin (or at least a way to check, if data is available for read).
This is not the same as a non-blocking read on the uart, but for most applications, this should be sufficient.