The only true definition of what a Chabad chassid is, is what the Rebbe has said. He is the only one who can really say what a chassid is. Because a chassid is a chassid of the Rebbe. That means that the definition of a chassid is one how has a particular kind of relationship with the Rebbe. In a relationship (any relationship) the relationship is defined by the partners in a relationship. Just as one cannot be married to someone who feels that they are not married to them - so it is with the Rebbe/Chassid relationship. A chassid who wants to consider himself a chassid of the Rebbe, must act his/her part of the relationship. He or she cannot unilaterally decide that they have a relationship without conducting themselves a the Rebbe wishes.
The following story, for me, is one of the most illustrative of how the Rebbe defined what a chassid of his is:
Dr. David Weiss has achieved world renown for his work in cancer research. Although he came from an observant home, his involvement in American culture presented him with many challenges. His encounters with Chassidim and the philosophy of Lubavitch helped him overcome these hurdles.Once while at yechidus with the Rebbe, he asked him if he could consider himself a chassid. "I am attracted to the Chassidic way of life," he explained, "but can never see myself donning a black hat or Chassidic garb. Does this disqualify me?"
The Rebbe responded, "When a Jew endeavors to take a step forward in the service of G-d and the love of his fellow man every day, I am happy to consider him my chassid."
Author: Yechezkal-Shimon Gutfreund