I was thinking that this might be the first time since 2005 that both the Nats and White Sox were over .500 on the same date, but I was way off. CWS had a good 2021, and were 1 game over .500 on 7/1 before really picking up the pace and ending 93 - 69. Niiiice!
White Sox also had a strong 2012, so both teams ended up > .500 at the end of the year. In 2005, the teams were a combined 105-57 at the 81 game mark as the Nats started 50-31 and the CWS were 55-26 on their way to the World Series. 2005 and 2012 are the only years both teams were .500 or better.