The choice of beige for the plastic cases used on popular 1980s retrocomputers was not arbitrary. As a color for a popular, mass-market, personal computer, it originated with the Apple ][, where it was specifically chosen by the designer, Jerry Manock.
In 1977, Steve Jobs hired Manock, a professional designer, to create the Apple II around Wozniak's electronic design. All choices, aside from the electronics, were made by Manock. This included the choice of a neutral beige color scheme - specifically Pantone #453.
The Apple ][ was the first and only personal computer of its time to be given this level of design attention by a professional designer, who would go on to design the Macintosh. It was the case then, as now, that Apple's great commercial successes became trend setters for the computer industry. The color of the original Apple II is the earliest example of this.
The major brands that followed Apple, such as Commodore and Atari, desperately needed to capture whatever "halo-effect" they could from Apple's early success. It's not any different than Samsung's following of Apple's smartphone design trend in the 2010's.
Some will imagine that this history ascribes too much credit to Apple for their contributions to personal computer design. After all, a color choice can seem pretty arbitrary, to a non-designer. To Jerry Manock, it is anything but arbitrary, and he deserves recognition for his contributions. You can read more about his contribution to early computers here.