Strictly speaking, they are no longer banned (and sneakers in specific colors have never been banned).
Previously, the NBA required players to wear sneakers in the same colors as the jerseys of the team in a given match. In addition, the sneakers of the entire team had to be the same color. Jordan violated this norm with his red and black Nike, which is written in the answer of Nikolai Chechulin (by the way, the story is actually a bit mythological: sneakerheads put forward the version that Nike very competently beat history with the Air Jordan 1, while Jordan was actually punished for other sneakers).
The rules now give more freedom. White, gray, black and team colors are allowed (not jerseys for a specific game, but teams in general) in any combination. It is no longer necessary for the whole team to wear sneakers in the same color - except that the left and right sneakers on the player should be the same. Moreover, the league singles out a bunch of exceptions from the rule. The current NBA champion is allowed to wear gold-colored shoes on the first day of the new season, the same is allowed in the playoff final for both finalists. You can do anything in the All-Star Game, and special colors are allowed to match the occasion, from Christmas to the Grammy and Oscars. Marketing much, huh?
UPD 08/29/2018. As of the 2018/19 season, all restrictions on NBA footwear color have been lifted.
Michael Jordan walked out onto the court in black and red Air Jordan 1. The National Basketball Association (NBA), to put it mildly, reacted coolly to the then innovative sneakers on the feet of a league rookie. This was because until 1985, all sneakers in the NBA were white. On October 18, 1985, the Air Jordan I was banned by the association for being "off-limits". As a result, the Air Jordan 1 in black and red was banned. Nike then immediately launched a multi-million dollar company to sell these sneakers, with the slogan that the Air Jordan 1 was so good that it was even banned, and willingly paid a $ 5,000 fine for every game Jordan played in the new sneakers while playing an advertising campaign playing up to this ban. But this is only the official story that Nike proposed to the public to advertise the model. As a result, Nike increased its sales from $ 870 million to $ 4 billion a year. However, not everything in this story was true.