Thinking about party loyalty

Let's say you have worked for Company A all your career and are completely proud and loyal to that company and brand, especially versus your competitor, Company B.

One day you learn that the CEO of your company has been embezzling funds. You also learn that he is unstable and has been making some truly awful decisions.

Can you not remain loyal to your company/brand while at the same time working to oust that bad leader and replace him moving forward with a good one?