There's a technique I've used for a similar requirement that doesn't require thermoforming or vacuum forming. You end up with a flexible, rubbery dome (or other shape per the mold).
The first step is to stretch a stretchy cloth material over the mold (needs to be a convex mold for this, where you can stretch the cloth over the outside). Stretch it where needed so that it is completely flat against the mold with no bulges. Cloth like old tee shirt material works well, and cotton absorbs well for the next step. Shapes with smooth, regular surfaces like domes work well. Something like a cube would probably require alterations to the cloth for it to lay flat on the form.
The second step is to impregnate the cloth, which holds it in that shape and gives it the plastic or rubbery feel. The form composition will affect what you can use for this, and whether you will need a release agent (never hurts). Here are some of the materials I've used:
Hot melt glue (generally use a metal form for this). Apply enough glue to cover the surface with a thin layer. Use the glue gun tip to spread the glue around. Then use a heat gun at a low setting to heat the glue to the point that it becomes watery (but not so hot that it scorches). The glue will soak into the cloth and the surface will self-level. When it cools, you have your shape. I sometimes turn it inside out, put it back on the form, and repeat the process on the other side. If you want a high-quality surface, turn it inside out when you're done, as the inside surface molds itself to the form and retains the surface detail and finish.
The result is flexible and rubbery but stiff enough to keep its shape. This is also a handy way to make small, formed things like phone covers. Large items the size described in the question would be flexible enough to fold within reason for storage or transportation. As long as you don't press a sharp crease into it, it won't retain the fold line when you reopen it.
Silicone caulk thinned with mineral spirits to paint consistency. Apply as many coats as needed to saturate the cloth and leave a surface layer. Then turn it inside out, put it back on the form and coat the other side to catch any spots without a good coating. The first side needs to cure to the point that it's stable (mostly cured) before flipping it to the second side, especially if you might stretch or distort it getting it off the form. Once it's finished, let it dry and cure for several days. Then remove it from the form and let it dry another day or two.
The result is very soft and rubbery. It will retain it's shape, but on something large, may not be stiff enough to not sag or collapse from its own weight without filler. It is soft and flexible enough to fold as needed for storage and transportation.
PVA glue. Thin it with water so it absorbs into the cloth. Once the cloth is saturated, you can add a coating of undiluted glue. This dries harder and less flexible than hot melt glue, but still flexible (i.e., not rigid) and strong. This might not be sufficiently flexible to fold for storage and transportation. But you could do something like cut it into sections joined by a hinge of the same (untreated) cloth.
I've also used this technique with other materials to produce a hard plastic or air-dry clay or cold porcelain shell, but those wouldn't be applicable to the requirements here. A single layer of cloth has always been adequate for my own needs, but you can repeat the process to add a second layer of cloth if you need something even stronger or more rigid.