Great question . -only happened to me once out of maybe 300-400 flights and I said I had a gig that night and couldn't risk it to which they conceded.
First, it is a possible risk of course as Airline have the right to refuse ANYTHING, and here is how to mitigate it.
One -if you don't bring on BOTH a "personal" item AND your guitar soft case -they won't bother you period -passengers constantly try to bring a 2 pieces of luggage as their "personal item" and "Carry on" -this pisses attendants off because personal items are intended to ride under the seat -but they are taking up 2 spots in the overhead -don't be that ******* -show them that you planned ahead -it's all about courtesy -as Lemmy once said "being polite and courteous doesn't cost a thing" -catch flies with honey -don't be rude EVER
Instead takes your IPAD, Laptop, Headphones, book etc and bring them in the cord and accessory pockets on the guitar bag -and put all your guitar accessories (except a pick if you get stuck at an airport) and check them in your luggage. If your Guitar case is your one and only item bringing on the plane they will not stop you. they will think you are a righteous dude.
Also, you want to board as early as possibly in your zone -if you are the last person on the plane it will be much harder -some airlines will let you board earlier for 20-30 bucks.
Lastly, you can call the airline and preset up the expectation you are bringing on a guitar and are concerned. Delta in the past has listed me as a musician with instrument needing to travel (sort of like one of those bull**** emotional support pets) in some kind of note on the ticket before -I'm not sure how it works, because like I said -I've never been refused but once and it only lasted a minute when I explained the importance of the item. Call the airline before you fly, explain your carryon/personal item are one thing and you want to make this easy on them and cannot check it due to value. they will tell you the plane type, the amount of bin space and amount of potential closets -and even how packed the flight is.
What Airline are you flying? if it's the right one -I might have some even better info for you.
This is the case I use the most below -it's an Access bag with rigged plastic around the headstock and butt -they go on sale all the time for sub 100.00 -see the 2 big pockets? thats where may laptop. Ipad, book and headphones, and good drugs go. in the little pocket I bring a battery and charger stuff and my VOX AC30 headphone amp. There are lots of other good bags too -just make sure they have padding, pcokets, and reinforced plastic ends -For your smaller Jackson you can get some really sweet carry cases -when I fly with my 335 or Starfire I have to use a larger gig bag which is harder
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Keep the questions coming! Let's get you to Asia in style.