A fabric-lined display cabinet is a different instrument from a mirror-backed one, and choosing between them is worth a moment's thought.
A mirror multiplies. It doubles the apparent depth of the cabinet and puts light behind everything, which suits cut glass and crystal - objects that are themselves reflective and gain from being lit from every side.
Fabric absorbs. It gives a soft, even ground with no competing highlights, which suits porcelain, silver, painted ware and anything with a shape worth reading. Against fabric an object has an outline; against a mirror it has an outline and a second confusing one behind it.
There is one practical consequence our master Indian artisans build for. A textile behind glass, in a room with daylight, will fade - not quickly, but before anything else in the cabinet does. So the lining is never fixed to the carcass. It is stretched over its own removable panel that lifts out from inside, so it can be recovered in an afternoon, decades later, without touching the cabinet.
Fabric or mirror, either is right. Only one of them needs planning for.