Religion
Some groups commonly referred to as 'religions' might only apply under def. 4 - certain kinds of Buddhists, for example.
What's your point?
(And wouldn't all Buddhists fall under at least the the third definition?)
Science does not recognize "truth" other than the kind involving accurate statements about reality.
Science is not concerned with the truth of statements that are not falsifiable ones about the empirical universe. It has nothing to say about other statements; it does not say that they are true or false, nor does it say that the empirical universe (which, incidentally, excludes logic and pure mathematics) is all there is to "reality". More to the point, science does not dictate any particular approach to spiritual, moral, or any other kind of non-empirical truth.
Unfalsiable claims are rejected in the scientific method. If the specific religious claims can be falsified (even if only in theory and not in practice), then your condition can be satisfied. If they can't, then they're not compatible with science. I win either way.
That's just not true, Melendwyr. The scientific method dictates rejection of falsified claims. It is utterly neutral toward scientifically unfalsifiable claims, since they are not within the purview of science. The scientific method is unable to falsify many kinds of claims, but that does not mean such claims are incompatible with science.
"Immaterial" is a meaningless concept. "Immortal", when used in the sense of "eternal and indestructable", is logically incompatible with the property of being affected by external forces and events.
May we all infer from the foregoing (non-)answer that you are unable to tell us how it might be possible to design a scientific experiment at least theoretically capable of unambiguously falsifying the proposition in question? In that case, perhaps you'd better retract your claim that the proposition is scientifically falsifiable.
Easy - God's activities were always confined outside of the observable and understandable causes that they accepted.
Not at all. Kepler, for example, likened the discovery of scientific explanations for natural phenomena to "thinking God's thoughts after Him". At the same time, such people thought they perceived God's supernatural activity in such spiritual matters as salvation, redemption, etc., which certainly do not correspond to scientific gaps.