Would removing the back-board of cupboards help against mould/mold?
They are structural, but if you leave the mounting rails at top and bottom, the middle could be opened, if the cabinet have a normal load.

A full back helps resist racking.  Its less important if several cabinets are attached together as a group.

Of course, exterior water intrusion is your real culprit and the best focus during the spring: downspouts and reversed grade toward house are the two most common causes.