Pretty crazy looking at the fangraphs injury report. Few teams that really rival the Sox in terms of volume of guys injured from my quick perusal. 20 DL stints for the Sox (13 currently). Six of which are 60-day, and with one guy maybe headed for 60 day (Grissom).
White Sox have 19 DL stints. 19 for the Athletics (10 current). 16 for the Yankees (9 currently, 6 on the 60 day), but with the exception of Cole and Schmidt, mostly to relief pitching depth. 17 to the Rays, 7 currently (most of their injuries occurred in March, and their guys were largely back by May). Rangers have had 19, with 12 guys currently injured, NINE of which are on the 60 day IL). Giants also have 20 guys who've hit the IL this year, with 7 of them on the 60-day.
So the Sox aren't uniquely injured, but they're definitely at the bottom of the barrel in terms of volume of guys who've been on the DL and number who are currently on the 60 day. Unsurprisingly, the list of teams with the most injured guys has a lot of middling-to-bad teams.
The difference between 20 and 15 or so may not seem massive, but when you consider the Sox have lost 3 starting pitchers (Giolito, Whitlock, and Murphy), two starting position players (Story and Casas) and Grissom has effectively been on the 60 day DL, it's starts to seem pretty insane.
https://www.fangraphs.com/roster-resource/injury-report?&timeframe=all