I don’t have a definitive answer on this, as there has been MUCH debate and controversy over the subject of alcohol stoves.
The SAFE answer is to bring a compressed gas stove — this is clearly allowed. Alcohol stoves should be fine anywhere that campfires are allowed — which is typically below 10,000 feet. This isn’t too much of problem on the first half of the JMT (assuming a SOBO direction), but is more challenging on the second half — where the elevations are higher.
I suspect that many people have used alcohol stoves on the JMT without any issues. Personally, I’ve never had a ranger come into camp at dinner time, so the chances of them knowing (unless you told them) is quite low.
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