Let me start from first defining on what does anti social mean.
Anti-social behaviours are actions that harm or lack consideration for the well-being of others.
Look at what happened in Italy the Governor went blatantly against the common sense of social distancing. Sending a very wrong message as a leader. Another, great example is of the British Prime shaking hands with the patients infected with Corona Virus. In turn creating a huge fiasco as well a huge risk for the whole society.
Should they not be classified as anti social just because they hold a senior position in the government? Many will argue that the people themselves should have taken care of themselves. But, lets remember most of the followers are gullible and they take their leaders world for granted. Like the governor might have taken their medical strength for granted. In turn leading to destruction of the country.
While the idea is not to make a political post but to draw similarity in an organizational situation. Similarly, any company has some anti organizational elements that are just concerned about their well being. Many organization in the past have fallen prey to such people and led their organizations to disaster. Its, not necessary that the leader was the reason it can also be their confident not sharing the right information.
Similarly, we can draw a comparison from the people on the ground who give two hoots about the lock down. Going on the street, getting into masses and ignoring every directive which are essential for the nation. Finding, ways to bypass the rules. There “N” number of such examples.
In an organization you see some breaking the rules at times specially by some who part of the top performer. We all need a top performer isn’t it? We don’t take actions as need them even at the cost of the culture of the organization. Like, these masses or individual that are flouting rules in the lock down and can bring a nation down. So, can these people who break rules bring an organization down.
So what should be the way? Let it run the way it is and let the organization suffer. As, it is everyone expects an outcome within a year or two
Leave a legacy for other to come and take it up further. If you believe in this my suggestion would be to take a data based decision rather than depending on people’s perception. Decisions are not easy specially the tough ones. Second avoid employee that spoil the fabric of your organization.