It was never a problem. The LEDs have a reverse bias specification well over 5 V and we are using a 5 V supply.
The preferred LED driver, the MAX7219 - like the 74HC595 - does drive outputs both HIGH and LOW, so LEDs not selected will be reverse biased - in fact, if the wiring is wrong or the wrong polarity matrix is inserted, all LEDs are illuminated, demonstrating what would be the reverse bias. The reverse bias simply does not matter at all. 
Your diagram suggests using pin 1 of the Arduino. This is generally inappropriate on an ATmegaxx8-based Arduino as you would likely be using serial communications.