I mean, people hated the Heat in the early 2010s pretty much exclusively because of Lebron. Popular opinion recently began to root against the Warriors in large part of Kevin Durant's move there. It wouldn't be difficult to make a case that much of the dislike that exists for the Cowboys is largely due to Jerry Jones. So...yes, one person can make an organization immensely more hate-able.
I knew a Cowboys fanatic who would spend thousands of dollars on Cowboys merchandise a year, but stopped supporting them because of Jerry Jones. He said something along the lines of "Jerry Jones took the legend that was the Dallas Cowboys and turn them into a joke". He wasn't completely wrong, but I still root for them.