Unfortunately, they didn't have much info at the viewing window, just a sign that said which movie it was from and when they plan to put it on display.
However, now that I am home, I did a quick search on their site and they do have a little more info:
https://airandspace.si.edu/newsroom...-museum-welcomes-star-wars-x-wing-starfighter
The site mentions that the X-Wing will end up "outside the Albert Einstein Planetarium". The Planetarium is a separate building from the main museum, so it could be interpreted as the X-Wing will literally be outside. If that is the case, maybe it is made of more than foam and cardboard? Also, if this is the prop that actors were sitting in and crawling in and out of, it may be more robust. (This is all total speculation on my part!)
Incidentally, if you are in the DC area, the main Air and Space Museum is still closed and will be until next month for the renovations. This X-Wing is being renovated out at the Smithsonian's Virginia Air and Space Museum location (the Steven F. Udvar-Hazy Center in Chantilly, Virginia). I am a life-long lover of the Air & Space Museum in DC and somehow I had never visited the one out in Virginia. In my humble opinion, the one in Virginia blows the one in DC away! The actual Space Shuttle Discovery is on display, an SR-71, the Enola Gay, a Concord, the actual Apollo 11 landing module, and hundreds of other space & aircraft. All of it in a truly gigantic indoor facility. You really need to go there if you have not been.
https://airandspace.si.edu/udvar-hazy-center