I think the importance of blood relationships is antiquated. In today's society we are able to access transportation like never before. Due to this families have moved apart and have learned to rely on friends and neighbors. Blood bonds were important for inheritance purposes. In today's time, inheritance is usually split between family members not just handed out to the oldest son.
I come from a family that includes a stepmother, stepbrothers and other step-relatives. Although I'm not as close to my stepbrothers as I was to my late brother, my stepmother has been a wonderful friend and loving mother to me. Blood relationships tend to form a closer bond, but deep love can be felt with others in an equally strong manner.
It depends on what you mean by relevant. Medically speaking, there are a number of diseases and conditions that are hereditary in nature and that can be better treated early on if we are aware of the fact that they pose a threat to us. In that case, knowing about your blood relationships can be very important today.
Similarly, it is not a good idea to marry and have children with a person whose genetic profile is too close to your own as this can lead to an increased risk of birth defects. Again, another argument for the importance of blood.
On the social level, however, blood relationships have lost much of their importance. Although in some parts of the United States, status is still clearly attached to who you are and to what your family name is, in general we are defining ourselves more by our own actions. We create groups of close friends who function as a support system sometimes taking over roles more traditionally played by blood relatives. In a sense, we craft our own families defined by ties of emotion rather than ties of blood.