Personally, I haven't quite made up my mind. On one hand, I do not like the idea of not being in control of my own life. On the other hand, it's not like I'll really know to actually care in the end.
As for what I believe, I feel no matter what happens, everything is pretty much set in stone as far as a single timeline/universe is concerned. While I believe we can alter things, I am one who supports the idea of a multiple timeline scenario, especially assuming time travel will become possible.
I would argue that the difference doesn't matter, practically speaking.
It might be academically interesting to know for certain one way or another, but whether our reality is predestined or determined or voluntary, it doesn't change that I have the
experience of the capacity for choice. That's all that really matters, ultimately, for things that have no relevance to one's experience need not be seriously factored into one's decision-making process. If I were to definitively learn that I have no "free will", what difference would it make? I'm still going to experience making those choices, whatever they will be (or already are).
This rationale applies to other stances I hold, such as the existence or non-existence of supernatural deities, or whether my experience of reality is authentic or illusory. That God exists or not means nothing if God has zero apparent impact in my lived experience, and that my experience may not be authentic doesn't negate that my experience
feels authentic. The truth of any of these matters may inform how you go about making decisions, but you're still going to be making decisions anyway. So that doesn't change.
In terms of "academic interest", total free will is impossible, since we know we are influenced, to some extent, by factors and variables our conscious self may not necessarily be aware of (external factors, biological factors, etc.). So our choices are at least partially determined. Are we biological automatons, with consciousness as simply a very complex, yet nonetheless determined process? That's harder to say, though with neurological quirks and cognitive biases abound, then if we do have free will, it can't be said that our decisions are fully informed.
Predestination from a spatio-temporal standpoint is more probable than not, as well. If the entirety of space-time exists, then all of time is laid out. There is no "present", with time being constructed one "frame" at a time; all frames of time exist simultaneously, and what we call "time" is just the experience of flipping through the frames of animation in one direction. Under relativity, there exist no privileged (see: absolute) frames of references, so there being an absolute "present moment" doesn't seem viable.
A multiverse scenario may be a way out of this. But if a multiverse is just a continuity of space-times, which are all laid out in full, then the branching of outcomes into new timelines would similarly consist of a set of frames, which all exist simultaneously. At greater spatial dimensions, time (in the sense of linear progression of states) would not exist. So in this respect, a multiverse, finite or infinite, would be predestined.
Perhaps you could say that predestination concerns
all the choices we will have freely made. A timeline would consist of frames in which our every choice was voluntary. Though this may get complicated if you were to gain foreknowledge of your future (voluntary) actions. If your (voluntary) present self saw your (voluntary) future, then this future would have to have already accounted for your past self's reactions and subsequent actions faced with this foreknowledge. Would you really have free will if your future was preordained?
It seems I go on and on, but I nonetheless say that even if the above is true, it doesn't change that we have to experience going through it anyway. Which is rather much a relief, since I don't have to think about my determined timeline (unless that determinism becomes directly relevant to my decision-making).
As an example of the above paragraph with the Grandfather Paradox, let's say a time machine was invented before my birth. Now let us assume I go back to a time period that predates my birth and I decide to assassinate either my grandfather or one of my own parents. According to the paradox, I should no longer exist because I'd have prevented my own birth. However, I would have created a history in which said parent/grandparent was murdered by me, an existing entity. Logic suggests that I wouldn't just simply disappear, since I'm clearly there, but instead I'll have created a different timeline where I will not be born despite the sudden existence of my future self in that point in time, if that makes sense. As far as history will be concerned, my future self appeared suddenly, spawning from thin air, and will be the only one of my kind, until some other yahoo from the future appears out of nowhere to commit a similar action.
I'm savvy on topics of temporal phenomena and paradoxes and the like (mostly through sci-fi media and layman's physics). So I understand full well the Grandfather Paradox.
There are different ideas concerning time-travel. There is the
Novikov Self-Consistency Principle, which is a form of retrocausality. You can't change the past, because your time-travelling self is the one who cemented your future of origin. So in such a case, if you tried to go back and kill an ancestor of yours, the very fact that you exist in 2014 means that you failed to assassinate them in the first place. It's not that the universe is conspiring against you; it's that your time-travelling self was part of history to begin with.
Your posited scenario is standard multiversal timeline-branching, and is a solution to the Grandfather Paradox. Since paradoxes are contradictions, what might reasonably happen if timeline branching doesn't occur? It would cause a superposition of timelines, I would imagine. If you go back and kill your grandfather, then you never come to be; yet how can your grandfather have been killed by you if you never come to be? Perhaps both outcomes exist simultaneously, or repeatedly co-cause one another, or something similarly zany.
I also wonder what might reasonably happen should I perceive my own predestined future. That future will necessarily have to account for my present self's witnessing of it, and the reactions and subsequent actions that follow. If this future will have accounted for any and all impulses to avert or ensure, or do nothing faced with this knowledge, what would this future look like? Interesting stuff to think about.