Fabric panel? Could you provide a picture?

It looks like textured ceiling, but it's actually kind of like a foam panel. If you push against it it will indent.

Sorry that I'm responding to your question so late, just ran across this forum.

Back in the early days of mobile homes after HUD issued its Construction and Safety Standards, the most widely used product used, that matches your description, was Armstrong Phase 5. It's simply a fiberboard panel, 4' wide x 12' or 14' long. The battens located every 16" oc are plastic. (Main purpose was to hide the staples used to hold up the material to the bottom chords of the trusses).

Replacement will be very difficult. I would recommed painting the panels if they're not too warped.

If they are slightly warped, an old trick was to reset the panels and, using braces, force the panels back into shape. This usually requires several days to allow the panels to dry in their new shape.

If they're badly warped, your only real consideration is to overlay with new materials. I'd recommend a fiberboard to keep the weight down.

I'm not certain I'd recommend gypsum drywall. What was used back in the day was a 5/16" thick board, especially manufactured for mobile homes (used high strength binders). These were usually screwed to the truss bottom chords with a number 8 clutch head screw and a plastic "rosette". The use of 3/8" drywall may prove to be too heavy for the trusses used in your home.