I do not reject non-naturalistic causes for the origin of life.
First, because I believe God created us, that means I affirm that God (a non-natural entity) caused the first life along with everything else. Whether the first life arose by natural or non-natural mechanisms (or a combination of both) its cause is absolutely and entirely dependent on the great Non Natural Cause: God.
Second, the God I find in scripture does at least occasionally intervene by first cause in this world (e.g. the Resurrection). I know of no way that science can rule out this possibility in any event in the distant past. So science certainly does not rule out the possibility that God created the first cell in the origin of life.
Third, science is very far from demonstrating that the origin of life by exclusively natural mechanisms is possible. Even if they could, this would not negate either non-natural causes or non-natural intervention. But they have not even shown this is possible yet. So I think belief that God intervened to make the first cell can be warranted. Nonetheless, just as James Tour explains, I do not feel anyone has demonstrated that the origin of life by exclusively natural mechanisms is impossible, either. So we are facing a mystery here.
In those three senses, when considering the precise truth of our origins, I certainly do not rule out non-natural mechanism or causes. I never have done so. On the contrary, I affirm and embrace God’s purpose and action as the important ways to think about the origin of life.
Not at all contradicting or denying these affirmations, in “science” we do not consider non-natural causes of things. So science never speaks of these possibilities. That does not rule them out, but it does silence science in these possibilities. But I think you are asking what I think (as opposed to what “science” says), so this is probably an irrelevant point.
And yes, I have explained this many times. It is nuanced position, but I hope this is clear enough to understand it.
Now, what are the two definitions of IC? And which one do you use?