Alternative is a very vast and relative concept, as is being supportive to a child. Children are easily affected and manipulated by their environment and especially by friends and pop culture. As parents we ought to guide them to understand how to make the right choices in life because we wont be there for them forever. We can't shield them from the environment we have to teach them how to survive in it while being true to themselves. Alternative music hairstyle or clothing is not an issue because for most children it is a phase and the society they live in will force them to conform by the time they become responsible adults if they want to move up the corporate ladder.
For other children who feel the urge to continue to express themselves that way well into their teens and adult life, it shouldn't be an issue if they are functioning happy members of the society. What parents should not be supportive in is giving children too much leeway to do things that would hurt them, their families or the society.
Parents have to be cunning and smart enough to get through to their children so that they themselves will know REASONS behind the FAMILY decision. Children now a days at a very young age are very worldly and opinionated and not doing something just "BECAUSE I SAID SO" wont cut it. You need to be patient enough and willing to repeat explaining over and over again why some alternative lifestyles and practices wont be allowed in your household or outside when s/he is old enough to get out.