If I understand your question correctly, by the terms “socially and publically” you are describing an individual who is not only selfish and thoughtless (or, uncaring) when alone (that is, privately) but also a person who is willing to display those same inappropriate attitudes toward others socially and enact those behaviors publically.
Though you mention that you feel that the term “antisocial” describes a “mental state rather than behavior,” it is in the nature of things that the thought process precedes the behavioral enactment. What is important in differentiating the average citizen behaving badly from the antisocial citizen behaving badly is a prevalent pattern of such behavior.
What follows is a rough hierarchical list which proceeds progressively from the least troubling, least serious mental attitudes (which, remember, usually result in bad actions) to the most serious mental diagnoses and correspondingly bad actions.
1. Selfish adjective: (of a person, action, or motive) lacking consideration for others; concerned chiefly with one's own personal profit or pleasure. (google.com)
2. Uncaring adjective: uncaring not displaying sympathy or concern for others. (google.com)
3. Moral turpitude: a legal concept in the United States and some other countries that refers to "conduct that is considered contrary to community standards of justice, honesty or good morals." This term appears in U.S. immigration law beginning in the 19th century. Moral Terpitude
4. Antisocial Personality Disorder: Antisocial personality disorder is a type of chronic mental condition in which a person's ways of thinking, perceiving situations and relating to others are dysfunctional—and destructive. People with antisocial personality disorder typically have no regard for right and wrong and often disregard the rights, wishes and feelings of others.
Those with antisocial personality disorder tend to antagonize, manipulate or treat others either harshly or with callous indifference. They may often violate the law, landing in frequent trouble, yet they show no guilt or remorse. They may lie, behave violently or impulsively, and have problems with drug and alcohol use. These characteristics typically make people with antisocial personality disorder unable to fulfill responsibilities related to family, work or school.
Antisocial Personality Disorder
5. Sociopath noun: a person with a personality disorder manifesting itself in extreme antisocial attitudes and behavior and a lack of conscience. Sociopathy
6. Psychopathy noun: (aka–-though sometimes distinguished from–-sociopathy) psychopathy is traditionally defined as a personality disorder characterized by enduring antisocial behavior, diminished empathy and remorse, and disinhibited or bold behavior.