If there is a reality that encompasses or is separate from our space-time and something in this reality can manipulate our material world then it is at least in principle measurable and thus knowable.
First, I'm not suggesting the ongoing manipulation of the material world (or Universe) by an outside entity or some influence by an outside reality.
What I think you're suggesting here, when you think about it, is that everything is knowable, even given our constraints as four-dimensional beings. The corollary to that would be that if something isn't knowable, then it doesn't exist.
That's a huge expansion of the realm of science, IMO, and neither necessary nor indicated.
Whereas if this particular something from outside our space-time cannot (or does not) influence our material world then there is nothing we can know about this entity or this reality. It may exist or not but in each case it is of no importance to our reality.
"Of no importance?" Again, isn't this just an assertion?
And to say that there's "nothing we can know" is really an overstatement of the limitations of scientific knowledge.
I'd like to suggest that your remarks here are not agnostic.
What I think you're suggesting here, when you think about it, is that everything is knowable, even given our constraints as four-dimensional beings. The corollary to that would be that if something isn't knowable, then it doesn't exist. No, that's not what I meant. I only said that if the existence of something is per definition not knowable then it is tantamount to not existing at all. It could very well exist but there is no way we could provide evidence in favor of its existence. If we assume that there is no way we can leave our space-time then under this premise we cannot detect whether there is something "out" there or not. We have to wait until this something from outside our space-time influences in some way our reality. Only then we are at least in principle able to know of its existance (if we didn't find a satisfactory naturalistic answer). I don't claim that in this case we understand this... well whatsoever, I only mean with knowable that we at least know of its existence.
Take as an example the inhabitants of a two dimensional flat-world. If we didn't interfere with their world (e.g. poke our fingers through their plane) there is no way for them to know of our existence and whether we exist or not would have the same consequences for their world. Now if we interfered in their world they could at least infer the existence of someting outside their particular space-time (if you poke your finger through their plane they'd see slices of it in their world) even if they cannot imagine higher dimensional objects.
Well, I think this is as agnostic as it can get.
Of course theologians and philosophers can theorize as much as they want about this extra space-time reality but there is no way how to test their inferences on this matter. One can only determine if one "hypothesis" (in lack of a better word) is more appealing to oneself than an other. That's how I see it but of course you are entitled to your own oppinion concerning this issue ;-)