Chess has been played using various pieces in some form for possibly 1500 years, the pieces representing the society it was in and made from easily carved materials that were available. This was common to pianos and other musical instruments, where Ivory and Ebony was used to easily distinguish colours in poor light that was common, so you wonder why modern ethic pianos don’t have a set of black notes with white notes in between. To distinguish the two sides they were in most cases made from different coloured material. Traditionally white pieces were made from ivory or boxwood and black pieces made from ebony. The black stayed black and the white went yellow, so an old set would be yellow and black, after about 1830 the convention yellow going first. The first surviving book on Chess was Repeating Loves and Chess Art by Luis Ramírez de Lucena in 1497 that showed white and black pieces. To remove any value reference other than an intellectual one of equals they were commonly stylised, so a black king had no more value than a white king. As it was a common game in Muslim countries it is thought that a stylised version came about due to the laws on idolatry there.
It was an arbitrary convention that was decided upon in the 1800’s that had been around for decades, people who commonly played the game deciding, and a person picked a hidden piece at random and whoever chose the white had that side of the board and went first. Queens or the ruling female starts on their own colour, whereas a King had to take whatever colour he was presented with. Obviously this is discrimination against men, not being allowed to start on their own colour, or discrimination against women who were told their place on their own colour, next to the king or vice versa. The rich landowners and bishops putting the commoners in danger first and easily disposable, having little freedom of movement compared to the upper class with the Knights doing decidedly odds things, but knowing a few people that the various governments have chosen to give knighthoods we aren’t a bit surprised.. There are so many things wrong with the game on so many levels if you decide on it.
To be fair in our modern society any piece of any colour should have totally free movement and be allowed to start anywhere on the board supporting either side. To stop aggression though they won’t be able to take or threaten any other piece. For a multicultural board all the squares must be of a different colour and different sizes and I’m not quite sure that they should be squares or limited to 8 x 8, as that implies they must fit in.
If you have a board that doesn’t have colours but symbols it is open to whoever wins the random selection.
Ivory and ebony was discontinued because of the endangered species act and quickly removed from production, but a small amount still persists, mainly in repairs, but Ebony also has the disadvantage that its dust is toxic.