The irony is it has helped me win employee trust. Managers have breathed a sigh of relief that they can shed their problem employees. Whole departments very clearly trust me more because this place is a better place to work now. Every one of the employees fired were making the work environment harder for everyone.
Prior HR seemed to have an aversion to terminating employees who deserved it and often there has been no documentation of corrective action even though these problems have been happening for years. I have basically been doling out corrective action, PIPs and terminations on a weekly basis.
Got rid of a major bully, a sexual harasser, a couple of very negative people, several people who called out a lot and left everyone burdened and a director who was a great person, just a very poor leader. The last was the hardest, and it really hurt my heart but that department has absolutely thrived with new leadership.