Does this fallacy exist?

As I understand the situation, it seems that X claims to vote for the option (s)he considers the “better” one, not necessarily an ideal one.   X then presents  a binary example: A & B (perhaps based on the US political model).

Y then hypothesizes an example that includes neither A nor B but another binary pair (C and D) — options that are somehow “worse” and less desirable that A and B.

It’s not clear what the “What if …?” question asks.  Is it (1)“For which of C or D would you vote?” or is it 2) “Does that mean you would abstain because A is not in the running?”

If we take X purely at the initial “I'd only vote for A” statement, X’s logical reply would have to be “I wouldn’t vote because A isn’t running.”

If we take X’s initial statement to mean (s)he would vote for the option considered the “better” one, even if not ideal, then C’s logical response would have to be “I’d vote for the better of C or D”.

Regardless, there’s a bunch of information missing, either in the description or the discourse between X and Y.  Without that information, it’s not possible to accurately identify fallacies.

There is one huge logical flaw, however — the assertion that Y is wrong!  From the description provided, Y’s sole input was to ask about an associated, hypothetical situation.  Y’s question may or may not be welcome … but asking about a parallel situation can’t make Y wrong!

H opefully, Y is interested in understanding X and looking for common ground … as opposed to just picking holes in what X says.

I think either one of these speakers could be committing a fallacy, but the slice of the argument provided is a bit too narrow to determine which one it is.

X says they'd vote for A, a candidate they don't like, because they're the lesser of two evils. When Y presents the hypothetical of an election between C and D, who maybe in this scenario might be Hitler and Satan, Y could be trying to tease out whether X's lesser of two evils calculus holds in all scenarios, or whether there is some line in the sand beyond which a candidate couldn't possibly get X's vote. I think that's a legitimate line of inquiry. But, they also could be setting up for a false equivalence , such as "You would vote for A, but you would also vote for Hitler."

When X responds to this, it looks like they are avoiding the issue . They're not actually addressing the hypothetical Y presented. However, it could be that they do have a line in the sand which they're just not articulating well, or that they're trying to keep the argument from going off topic and want to stick to the differences between candidates A and B.

First of all, “A” is singular, not a “them.” However, ignoring the politically motivated pronouns and bad English, one obvious fallacy is that of diversion. The Fallacy of Diversion is when one party attempts to divert the discussion to something more comfortable when he has no answer to the topic at hand. This is a  verbal slight of hand. There are others. 

Y claimed C and D are worse than A and B.
X agreed that "C and D are worse than A and B". How is this asserting that Y is wrong? Wrong about what?

X refused to engage in the hypothetical by responding with what seems to be a nonsensical response - like they did not understand what Y had said.

No fallacies here, just poor communication.