Sikhism is viewed as a religion with many virtues and the ones that live by present humility and experiences that are long-lived in people's mind.
Sikhs are proud of speaking the truth, having patience, being kind and humble, having love for fellow humans. These are the very basic tenets that are incorporated by Sikh Gurus. The fact that one wears a turban is a physical attribute that shines these virtues of Sikhism. Sikhs are often proud of leaving these impressions.
Here is one story that touched my soul prompting this post.
Few years back a fellow Sikh ended up cutting his hair. He had found that he had and early stage grade II brain tumor which had to be removed. It was at that time he removed his hair and beard (knowing the risk factors or recurrence This change was a very emotional decision as he had never cut his hair or beard. It was a pragmatic decision (for his existence) but what would follow was beyond reckoning. He had also cut his son's hair after this incident (for his family's equilibrium).
He kept his health condition in confidence. When he met his fellow Sikh friends they threw him under the bus immediately. Few cried siting loss of a Sikh from a community. His son, an active participant in Sikh communal activities was asked to leave these activities. Activity organizers felt that other kids might follow and cut their hair as well. He was removed from practices and shunned out.
While the family was tackling health issues, the antipathy from the Sikh society made matters worse for the family. These Sikh individuals obviously had forgotten the many virtues. I am not saying that cutting the hair was right. I also don't agree with the communities reaction drawing disdained feelings at a time when the Sikh Virtues were needed the most.
Practicing Sikh virtues is far more important that showing the color of Sikhism through physical attributes. If one looks like a Sikh does not mean that they practice the virtues. To that extent, there may be many Sikhs that practice these virtues that may not wear turbans.