On the Fox game last night, one of the announcers mentioned that the White Sox had only a .390 winning percentage against teams with a .500 record or better. That, they suggested, could be an issue in the playoffs (the Sox were 16-25 entering last night's game in these cases but now they are 18-25 for .419).
The other likely AL playoff teams are doing better than the Sox (all through last night)
Red Sox 33-25
Rays 37-27
Astros 43-23
A's 27-30
I looked at all the playoff teams from 1995-2019 using Stathead, the searchable data base run by Baseball Reference. I found that 59 of the 216 teams that made the playoffs had losing records to teams that played at least .500.
12 of those 69 teams made it to the World Series (20.33%).
38 of the 157 teams that played .500 or better against teams that themselves were .500 or better made it to the World Series (24.2%).
So there is a slightly better chance to make it to the World Series if you can play at least .500 against teams that played at least .500. But it does not seem like a big deal.
The lowest winning percentage against teams that were .500 or better that made it to the World Series was .400 by the 1997 Indians. There was a .420 and two .450 cases (who both won the series, the 2006 Cardinals and the 2010 Giants-5 other teams that had losing records in these cases also won the series). So the White Sox are still on the low side but this season is not over yet.
3 of the 16 teams that played exactly .500 against teams that were .500 or better made it to the World Series.
Update July 19: The teams that played at least .500 against teams that were .500 or better had an average overall winning percentage of .590.
The teams that were under .500 against teams that were .500 or better had an average overall winning percentage of .561.
So it is not surprising that playoff teams that played .500 or better during the regular season against teams that were .500 or better are more likely to make it to the World Series than teams that don't because overall they are better.