The discomfort in accepting these statements as true can be taken as evidence that classical propositional logic can diverge from human intuitive or verbal reasoning about implication (whether with a causal narrative or not).
In this case the constructive [as in "constructive mathematics" or "constructive/intuitionistic formal logic"] meaning of $X \implies Y$ is closer to the mark: from a proof of $X$ we can construct a proof of $Y$, or less formally, knowledge of $X$ can be correctly transformed into knowledge of $Y$. It is not equivalent to the classical forms with negation, such as "(not $X$) or $Y$", or "not ($X$ true and $Y$ false)", in the absence of excluded middle or some other nonconstructive reasoning principles. The second form means the implication is unfalsified and the conversational intuition about the $X/Y$ statement is more that it could be falsified by doing $X$, than that it must be equivalent to the implication being true (simply because classical rules for manipulating the words AND, OR and NOT would say so; maybe the rules don't apply or we feel that they don't).
There are interpretations in modal logic (which is also related to interpretations of excluded-middle free logics) as the statements are time-dependent or contingent on the past doings and not-doings of $X$. I am not familiar enough with modal logic to say whether this would be more convincing than the constructive interpretation.
It seems correct conversationally to call never instantiated statements (vacuously) unfalsified or untested, but not vacuously true.
The statement would be vacuously true in cases where the status of $Y$ is known to be independent of knowledge about $X$. For example,
"every time I went to sleep, the sun rose the next morning"
should be true and not only unfalsified, if we have reasons to accept that the sun will rise in the morning no matter whether particular persons sleep or not during the night. This holds in any non-classical logic that I can think of, and it makes perfect sense conversationally: an implication is vacuously true or vacuously false if its premise is irrelevant to drawing the conclusion.