Why using resistors with the MAX232 chip?
Safety or EMI (Electromagnetic interference) reasons I'd guess. If you have the resistors, you won't be able to kill the PIC if you set the serial port pins to low.

The application note uses 3.3 V supply, so if we configure the UART pins as low, we'll get at most around 8 mA of current, which should be safe for microcontroller to sink.

Also the resistors slow down the signal edges a bit, so there's less EMI.