First, what are the pillows stuffed with? A solid foam block is most common, but some use small foam pieces, and one cylinder shaped pillow on my Eddie Bauer even has excelsior (small wood chips) down feathers? Not likely in an Airstream. Poly fill down substitute? Probably not... that is usual for bed pillows, not decorative ones. It is very common to have dry clean only fabric over fill that should not be dry cleaned at all. Your carpet and upholstery cleaning services can use foaming cleansers or "steam clean" the pillows, or you may be able to remove the covers for cleaning.
Of course there is no guarantee that your pillows are constructed the same way mine were, but LOOK at all four edge seams, and if one has a top stitched seam set very close to the binding (round trim piece) that is the seam which was left open until after the pillow form was stitched inside. Use a thread picker to remove that seam, pull the form out and dryclean or launder the cover, then restuff the pillow and resew the seamusing a zipper foot to get close to the trim. If you don't sew, perhaps you can find a neighbor or friend to help.
OTOH, just replacing the pillows is not a bad idea. Airstream does not use the highest quality foam or fabric, or even fabrication.... so redecorating is definitely an option.
Something I picked up here: I've reupholstered and slipcovered several pieces of furniture, but never thought about the difference between fabric for a cushion (top, side and bottom pieces) and a square or rectangular pillow (top and bottom piece only). Mass manufactired pillows have "ears" or protruding corners because the fabric is cut and sewn with square corners... and the cushion doesn't fill them because it is tapered at all four edges. Really beautifully tailored pillow covers are cut with corners that are tapered inward gently. If there is an absolute formula on how much to taper the corners, I am unaware of what it is. On a 12 inch square pillow I usually take about 1 inch out of the last 3 inches of each corner... more for a very thick, firm cushion. I use a French Curve to draw then sew the corners consistently.
Well TMI again. Too many choices.
Today is a gift, that's why they call it the present.