No, but if they don't agree with their group's actions they have a responsibility to either split off from the group (if the group is the majority) or denounce the group (if the group is a minority).
To use Islam as an example, actually read a study a few years back that basically showed most Muslims identify first and foremost with their faith. Thus they see themselves as Muslim before any nationality, career or other personal trait. The study posited the lack of backlash to the fact that, however much they may disagree with the terrorists' actions, they still at some (sub-concious?) level relate to the terrorists more than the victims; simply due to their shared faith.