Resistors in serial communcation
Regards your schematic, I think the reason might be is to avoid two data transmission chips/systems clashing or fighting. It appears that if the external TX pin is active then it will win the battle to talk to the chip on the right i.e. the chip on the left is defeated.

Other uses of resistors in series with data transmission output pins are usually to provide impedance matching and to prevent reflections - they are usually in the range 10 ohms to 33 ohms.