Part of the problem here is the confusion over NMEA and RS232, 422, or whatever.
When you send NMEA data to a device, those data come FROM the NMEA output, +, or -, to a NMEA input, + or -. NMEA is NMEA, NOT RS anything. Serial communications protocol specs...baud rate, stop bits, etc. have no meaning whatsoever.
Yes, you can convert, but you can't just plug an NMEA output into an RS input or vise-versa no matter how you jiggle the wires.