Well, that could be answered both yes and no. Do we believe in the biblical concept of predestination? Yes. Do we believe in the Reformed or Calvinist corruption of this biblical term? Absolutely not. Further, any hybrid of these two is fundamentally impossible.
What we deny as Apostolics is not predestination but “unconditional predestination” but would instead embrace the biblical view of predestination which is based on God’s foreknowledge of those who will freely respond positively to God’s free gift of grace through the prevenient enablement to do so. That means God has provided both the means (capacity to choose God) and the opportunity (Christ’s atonement as man) to be saved, and the human component is to accept what is freely offered. So we believe in “conditional predestination” because Scripture shows God freely limited Himself by giving humanity the true ability to choose Him or not. What’s at stake here is misdefining the term predestination which has led people to create theological systems that defame the character of God. We as Apostolics reject unconditional damnation. Because we deny this on biblical grounds, we must then also deny unconditional salvation or election. These are inexorably connected.
With the rise of post-fundamentalist Reformed evangelicalism, we as Apostolics (as well as others who classically call themselves Arminians) have been under intensifying scrutiny and often withering caricatures and misrepresentations of our biblical beliefs. We have been increasingly dismissed in evangelical circles by these mostly uninformed misrepresentations of our views instead of being directly quoted ourselves. This has made some Apostolics respond in an almost knee-jerk reaction by dismissing theological terms for our biblical position. It’s fascinating to see Apostolics distancing themselves from classical theological and biblical definitions that have always been part of our beliefs such as: Arminian, predestination, fundamentalist, dispensationalist, etc. This is, in the author’s opinion, from pressure to conform to the prevailing theological sentiment for inclusion and respectability. We shouldn’t cave in to “theological peer pressure” and give up these scriptural terms and concepts but demonstrate how these biblical terms are correctly defined.
Some have suggested our view started with Joseph Arminius, and this “new” invention of Arminianism shows Church history is against us because it came after Calvinism. But the simple fact is all of the Greek Church Fathers in the first couple of centuries, even many medieval Catholic theologians, as well as many reformers before Arminius (such as Philip Melanchthon) held this view. So our view is biblical first of all, and second it was the prevailing view right after the Apostles and continued even when Reformed theological ideas moved away from these biblical definitions.
Apostolics must make sure we do not let people misdefine our beliefs and by this misconstrual strip away the terms we use to define ourselves. The reach of Reformed theology and its prominence in evangelical circles have made some desire to make Apostolic beliefs more palatable or compatible with Reformed approaches. We need to understand that is fundamentally impossible. One approach is biblical. The other defames the very character of God.