The MAX232 is used for RS232 communications. As for your Allegro 6276 it requires logic level signals not RS232 level signals. As such the SERIAL DATA IN,CLOCK and LATCH ENABLE signals on the 6276 connect directly to the port pins on your 8051. It is not necessary to use the serial uart feature of the 8051 to interface to the 6276 - you can use the normal port pins and write your code to shift the bits out to the 6276.

Don't get confused with the term 'serial' - you have serial comms to your pc (RS232) which is actually asynchronous serial whereas the serial to the 6276 is synchronous serial as you supply a clock signal to shift the data in.