Apple - Is it possible to override the SD Card write protection setting in software?

No. You cannot override the write protection status of an SD Card via software.

The read/write status is handled by the firmware of the SD card host controller not by the driver. From Toshiba (manufacturer of these chips):

Content protection can be realized by using the [controller] with firmware.

Inside the SD card reader are a series of pins that get connected if the write protection is enabled. This tells the controller that write protection is enabled (Picture is not of the MacBook connectors, but the best one to illustrate how it works I could find online).

It is most likely that these pins are "stuck" together causing the controller to "see" the card as protected. You can attempt to clean it out or as a better alternative, just purchase an inexpensive USB SD Card Reader.