DIAGNOSIS You're right to be cautious. Harsh chemicals or abrasives can damage the plastic interior liner and cause cracks or clouding.
FIX Unplug the fridge. Remove all food and shelves. Use a solution of mild dish soap (2 tbsp) and warm water in a spray bottle. Spray, wipe with a soft cloth, then wipe again with a cloth dampened with plain water to rinse. Dry thoroughly with a towel before plugging back in.
IF THAT DIDN'T WORK For stubborn stains or mildew on the seal, use a 50/50 mix of white vinegar and water. Apply with a cloth, let sit for a minute, then wipe clean. Vinewater is safe and disinfects.
HEADS UP Never use abrasive pads, bleach, ammonia, or solvent-based cleaners like acetone. They will permanently damage the plastic surface and can cause off-gassing that taints food.