If you are flying with it in the cabin with you, I would not worry. If you check it as baggage, definitely do so! A touring musician I know once referred to "airline baggage handlers, an other lower forms of life...."
Anything you can do to take stress off of the instrument in transit is a good thing, especially if the case is dropped or tossed. When the strings are in full tension, the entire instrument is under stress to keep from collapsing. A really fine instrument may be even closer to its tolerances than a cheaper one because lighter construction is what makes it responsive when played. If the instrument is stressed in transit in a way that adds to that pre-existing tension, the instrument could suffer.
I recommend dropping the tension by at least a third, a fourth is better. It won't hurt to try it, even if you don't think it is necessary. The worst thing that could happen is the strings settle a tiny bit when retensioned. That should not be a problem unless you are playing a quick concert in the airport lobby.
Like others here, I recently flew (SW) without incident carrying on a concert size fluke in its bag. Several on at least a leg or 2 had full size guitars in gig bags.
It did not occur to me to loosen strings then, nor had I ever done it with a guitar checked in as luggage in a hard molded case & taken to Africa, the Middle East, & Europe. It was fine. Lucky? I dunno. That's a lot of flights to be lucky on.
Someone ought to put this link in a sticky and label it "travel and shipping recommendation for a uke". I just would have assumed loosening the strings was better than shipping in tune. I am surprised it is the exact opposite. Good info.
I'm not surprised. Having used the search function on various forums, I have found it an intensely frustrating experience wading through a large amount of irrelevant material to not find what you were looking for.
The question to ask is, "Should you loosen the tension if you live in Denver?" The answer would obviously be no. Typical cabin altitude on an airliner is lower than it is in the mile high city.
Many tales on UU (markr1 comes to mind) about popping bridges when stored in humidified homes and in cases. So, the question to me isn't so much as whether one can fly, drive, store a uke with strings remained in tuned, higher tension position, but why not de-tune one or two revolutions? To save the wrist?
I've never done it either. Wouldn't hurt, but a modern instrument with secure glue joints and relatively young wood can take a little fluctuation.
But, if I was taking a delicate instrument, like a very old one, or an instrument otherwise compromised, i.e. cracked soundboard, noticeable bellying, loose brace,... I surely would lower the tension before flying with it.
Atmospheric pressure per se has very little effect on instruments; the biggies are rapid humidity change and actual physical shock. When I fly with my uke, I carry on and put it in the overhead. I never lower string tension. When I check guitars through, I just make sure the peghead is well supported to prevent whiplash events.
The relatively new major shipping issue we're seeing is that if we ship something to Canada or something comes back to us from the North Country, the customs idiots do not repack the box with proper packing material. They just toss the case in the carton and are done with it. It's caused some real problems.
The question to ask is, "Should you loosen the tension if you live in Denver?" The answer would obviously be no. Typical cabin altitude on an airliner is lower than it is in the mile high city.
Actually, it could hurt, according to the info in the Larrivee Guitars link that SailingUke posted. For anyone who didn't bother to follow that link: The gurus at Larrivee say it's a manufacturers' industry standard to always ship instruments with full, usual string tension to help keep the tuning gear-heavy headstock from possibly snapping off if the instrument is dropped in transit (because slack strings might allow that to happen). A guitar shop owner once told me another reason he always keeps displayed instruments in tune with normal string tension: Slackened strings could permit the neck to "relax" and begin warping. Isn't that also the rationale for the common recommendation to change strings one string at a time?