This article is a follow-up to the "RS232 and Raspberry Pi" (link)
The same MAX board that I had also worked with Arduino at 5V although it was designed for 3.3V operation (capacitors onboard were sized for 3.3V operation - page 10 of MAX3243 datasheet). Still, it seemed to work fine up to the 28800 baud rate. Any faster and the software starts detecting data framing errors and the data becomes corrupted.
However, that was purely a design limitation of that particular RS232 board that I had.
Given that I did not have a voltage level translator, I only connected the TX1 pin so Arduino would send, but not receive data. That pin exists only on Arduino Mega boards since that's the only board with more than 1 hardware serial port. I used a sketch "Examples -> Communications -> MultiSerialMega" from the IDE's set of examples. That code simply echoes anything that it gets on its primary serial port (TX0/RX0 or built-in through the USB) to the secondary serial port (TX1/RX1).