The referees are not biased against the Cowboys. That is, and has always been, a complete myth.
Take last season for instance. Yes, the Cowboys were the most penalized team in the league. However, as a group, the Cowboys had the 2nd most penalized opponents last season.
If you wanted to detect bias when it comes to penalties, you wouldn't look at a team's number of penalties and compare them to others. Instead, you would look at the penalties margin between a team and their opponents and then compare that margin to the other teams around the league.
For example, in 2021 the Cowboys had 127 penalties while their opponents combined for 121 penalties. That is a difference of six penalties more by the Cowboys for the entire season. Compared to other NFL teams that margin ranks them15th in penalty difference for the 2021 season.
The real imbalances are demonstrated by the Raiders and the Texans. Both were penalized 25 more times last season, than their opponents or almost a penalty and a half more per game. The Cowboys were penalized a third of a penalty more per game, the difference is hardly measurable.
The teams that seem to be more favored are the Bengals and Colts penalty margins of -44 and -33 respectively. This means that, last season, Bengals opponents received two and a half more penalties than the Bengals.
In addition, the penalties cannot be attributed to the current staff. A look at the ten year trend in penalties shows us that the Cowboys penalty margin of last season are consistent with their results over the past ten years. Over this period of time, the Cowboys averaged 0.3 more penalties per game than their opponents.
Looking further at the ten year trend, it is the Raiders and the Seahawks that were penalized more often than their opponents the most often, although Seattle did almost break even last season. The Raiders averaged more than one additional penalty per game than their opponents over this ten year period.
The teams with the most favorable ten year margins were the Colts and the Giants. The Giants consistently received less penalties than their opponents, almost one penalty per game over that ten year period.
This is why any claim that the Cowboys are being targeted by the referees simply isn't true. It certainly isn't reflected in the raw numbers.
So then, we still have the question as to why the Cowboys and their opponents have the highest combined penalties per game in the league for 2021. Over the past ten years the Cowboys and their opponents are ranked at #15 in this category, practically dead center so last season may have just been an anomaly. I don't have that answer.
My theory is perhaps the Cowboys and their opponents have a higher rate of being refereed by a stricter group. If the Cowboys were assigned this group 8 times and other teams were assigned an average of about 4-5 times last season then this might explain why both the Cowboys and their game opponents received significantly more penalties.