Most folding tables aren't really sturdy enough, very few card tables are sturdy enough, and plenty of people could be great quilters if their machine wasn't bucking up and down like a bronco! Some are ok, the office level heavy weight ones are essentially permanent when set up, but can still be folded down.
Something like a pre-cut shelf board can be enough extra stabilizer for a lighter card table, and it will be flat when the rest of it is folded down.
My current sewing table is the short return from a computer desk combo. It is office weight and pretty sturdy but even so my heavy machine likes that shelf board even if my lightweight machine doesn't notice or need it (it was so lightweight I finally used blue tape to keep it where I wanted it). We got it from Craig's list, it came disassembled, still heavy and awkward as heck, but doable.