yes, has to be E , as the answer to whether other corporations that own coal companies also own gas stations is irrelevant . C offers a precedent , which is obviously relevant .
In case there is still some ambiguity on why E is correct and not C, here is my take on it:
(C) Have other miners’unions won contracts similar to the one proposed by this union?
Since the question asks for the LEAST relevant to the Union's consideration, any information that is even remotely influential in going ahead
with the boycott can be considered as a wrong answer choice.
If we assume that other miners' unions have won contracts similar to the one proposed by the union, then it clearly indicates that their demands are not completely outrageous. Even if the answer to that question is NO, that would still influence the decision whether to go ahead with the boycott or not.
As rightly mentioned above, it will help determine whether a precedent has already been set or not. Since we are only looking for the LEAST relevant option, it makes answer choice C more relevant than E.
(E) Do other corporations that own coal companies also own gas stations?
To know whether other corporations that own coal companies also own gas stations is completely irrelevant. Had E stated "Does any other CORPORATION have gas stations in the locality/country/world (though farfetched)" would have made E more relevant than C. Because in that case, knowing that boycotting Gasco would have a significant impact since there would/wouldn't be other gas stations that consumers could go to. But in its current form, E is focusing only on corporations that own coal companies and whether they also own gas stations.
This makes E an obvious choice for me.
Hope it helps.