White-furred tauren are held in a more spiritual reverence within the Kalimdor tauren tribes. This tends to lead them into a path of spirituality and priesthood. However it is not required to connect with the spirits nor does it mean you have to become a spirit walker. When an all white furred tauren is born, they are often seen as an ill omen of times to come.
Highmountain tauren do not have white fur on their spirit walkers so it isn’t required to become one. It is just the Kalimdor tauren place a spiritual significance to that specific fur coat.
White fur among the tauren is kind of like golden eyes among the Kal’dorei. They’re a sign, a portent, but not always either a guarantee or a pre-requisite. Golden eyes among the Night Elves are supposed to signal druidic talent. Yet it’s Malfurion who was born without them that became one as opposed to Illidan who lacked the patience or the humility to do so…and ultimately had his eyes burned out.