The question is whether an "unstated implication" by Y that there is something "bad" about X because X doesn't view something as unethical the way Y does is a logical fallacy on Y's part or not? Furthermore, if Y is committing a logical fallacy what is the name of the fallacy?
One needs to find a criteria for saying something is a logical fallacy. For the purpose of this answer I will use Bo Bennett's three criteria:
- It must be an error in reasoning, not a factual error.
- It must be commonly applied to an argument either in the form of the argument or the interpretation of the argument.
- It must be deceptive in that it often fools the average adult.
Y's view of X may be a factual error rather than an "error in reasoning". By the first part of Bennett's three-part criteria, Y's factual error would not be a logical fallacy.
Since Y is not even stating the implication about X's view, Y is not applying the implication to an argument. By the second part of the criteria, Y's unstated implication would not be a logical fallacy.
If Y isn't stating something, it is hard to see how Y's thinking is deceptive, except perhaps to Y, and fooling the average adult.
By Bennett's criteria, one might suspect that Y's view of X is not a logical fallacy. It may be something else, perhaps a cognitive bias.
That Y's behavior toward X does not imply that what Y is doing is logically fallacious does not mean that there is no harm being done to X especially if X is later placed on the defensive. It would just not pass Bennett's criteria as a logical fallacy. Hostile behavior might be better addressed as hostility rather than trying to transform it into a logical fallacy.
Also, it doesn't mean that people have not tried to name such situations and called then logical fallacies. Bennett provides a list of what he calls pseudo-logical fallacies. The following might under certain circumstances fit the description of Y's behavior toward X given perhaps a more specific context.
Hifalutin’ Denunciations: Denouncing an argument or opponent with vague, pretentious, and grand-sounding generalized accusations. This is more of a type of rhetoric.
Bennet, F., "Pseudo-Logical Fallacies", Logically Fallacious https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/6/Pseudo-Logical-Fallacies