If the power supply is separate for the Display. then there will be no issue, the raspberry will not supply through the HDMI. If not connected separately, I will recommend you to connect it using a separate cable to power the Display and RPI.
If it again shows the power deficiency at the raspberry side, Then I recommend you to check the MAX232 again, is the MAX IC is heating up? There is a lot of chance the current is draining somewhere.
Can you share max232 ic to RPI connection?