Currently, the Tampa Bay Rays have the highest strikeout rate in the league, striking out 26.2% of the time. Since the postseason opened up to 10 teams back in 2012, only four teams (out of 50) have made the playoffs with a strikeout rate above 22%.
Those teams combined for a record of 10-14, with no World Series appearances. The only team to make it past the division series were the 2015 Chicago Cubs. However, they were easily swept in the championship series by the New York Mets.
No team has made the playoffs with a strikeout rate above 25% since 2012.