For centuries before ISIS ever materialized, organized extremists from various cultures throughout the world conceal their individual identities in order to remain fluid and seamless within society otherwise. One example would be the Klu Klux Klan, whose members quite often comprise local officials and entrepreneurs that thrive in their social network while also serving their collective extremist views as supremacists.
Like any other fundamentalist or extremist organization, its members are not only unashamed but are often indoctrinated to perceive their actions as direct preservation of idealisms under threat by any social culture or organization deemed unworthy through their seemingly antithetical composition. A belief of such intensity most always extends beyond instinctual human morality and into the realm of distortion of reality, typically being instrumented by one person or select group of persons that are gradually supported by followers whose impressionism often leads them to commit acts of allegiance considered by most to be incomprehensible in nature, i.e. Hitler and the subsequent genocide of Jewish people through various forms of extermination by german soldiers.
So the question of whether a moral impression influences ISIS members is answered by a study of historical patterns among similar organizations. As prosocial humans, we struggle to understand just how far the reach of extremism can go in the demonstration of unspeakable acts and in ourselves, believe that no human being could be capable of such without struggling to overcome shame or intense moral conflict.
It is not within the struggle of a moral framework that ISIS engages its policies but rather a singular idealism, an extremism void of any balance by moral virtue. The acts of violence toward transgressors are imposed purely as the most extreme measure believed necessary to invoke submission to a strict fundamental rule or law that is idealist in form, one that is unfortunately formed in the absence of recognition to human frailty.
The abandonment of some members to its extremism is also a manifestation that is strictly individual in context rather than any representation of the collective mindset which fuels or drives such organizations. It is understandable that a moral conflict can and does arise within its members, but again important to note that it occurs among its followers to the idealism rather than the founders.