In addition to cases where you do find someone/something unpleasant, you can use "敬遠" to describe situations where you avoid someone/something for other, less negative reasons.
One such reason would be that you consider the person as being out your league, that you are no match for them. Another would be that you find the thing alright, or even desirable, but the path you must take to get to it is not.
So, in the case of JDICT, to define "敬遠" simply and singly as "avoiding (something unpleasant)" would be to define it too narrowly, though not outright wrongly.
In fairness to them, however, I must mention that they also give the less-specifying second gloss "shy away from", presumably in order to counteract the over-specification of the first, or at least to properly widen the coverage. We would be wrong to judge them based on (the bad) half of the evidence.
As for goo辞書's case, I think "かかわりを持つことを嫌ってその物事を避けること。" leaves no room for fault-finding.
Unlike JDICT's "avoiding (something unpleasant)", this does not say the avoided entity is found dislikable (I fear "dislikable" might be too strong a word for "嫌って" here), but it's the having to do with it that it says is found dislikable.
And they would be right in this claim. "敬遠" does not entail that the avoider has a distaste for the avoided, but it is, I think, necessarily true that they find the experience that comes with having or being with or getting to it/them disagreeable or at least uncomfortable. This is the case even in situations where the person/thing being kept a distance from is regarded positively in some way. A couple of examples:
This sentence means the boys hold the girl in high estimation, but they don't feel comfortable at the prospect of dating her, or possibly talking to her or possibly, even, literally getting near her, because they think she is too good for them and they would feel like dirt next to her.
This means you've been interested in the cafe, but the travel there seemed like too much of a hassle to you so you've never popped in, until now.
The last example reminds me that 敬遠 doesn't always involve active avoidance, suggesting that translations like "avoid" (which I believe carries the connotation of activeness) might not fit the word's meaning sometimes.
Lastly and most importantly, about your interpretation of the use of the word in the quote. I can't say I'm absolutely certain, but I do tend to agree the text is commenting that there are probably some people who find sake (or some particular sake?) so daunting that they avoid it. At the least it is not indicating by the use of "敬遠" that said people avoid (some particular) sake because they find it unpleasant.
So in conclusion, I will say that your interpretation of the word, as I hope I've somehow managed to show, is entirely acceptable, and is not (entirely) at odds with the dictionaries' accounts of its meaning and usage.