In Taoism, there is no fated apocalypse. This is true across schools, including the 4 Ascendant Tradition, and traditions that are heavily based on oracle practices.
Humanity may ultimately destroy itself or may not make the correct moves to avoid destruction, but there is no divine apocalypse of humans. People ask this question largely because it is a dominant theme within Judeo-Christian tradition.
People become obsessed with it, because the thought of a great release (effectively a great correction of spiritual and relationship wrongs) is very appealing to many. However, this thought of a release is a great personal error in spiritual development and completely ignores most of the divine laws that underpin reality.
Taoism is driven by a belief in Free Will and Choice. These premises about our existence are inherently hopeful, because it means that humanity can determine its own direction. If we want, we can right our own wrongs.