Question re: Ring of Mind Shielding vs Forbiddance

This question is about 3.5 D&D.

Question: Does a Ring of Mind Shielding [DMG, pg. 232] protect against the effects of Forbiddance [PHB, pg. 232]?

Adjacent Question: Does the ring allow an evil NPC/entity to bypass a Protection from Evil spell effect?

Example: A 2nd level chaotic evil NPC wants into a room protected by a Forbiddance spell cast by an 11th lvl neutral good PC. Does an 8,000 gp ring protect me from the will save (or half) for 12d6 damage?

Rambling: The spell does damage based on differing alignments, and the ring provides immunity to "any attempt to magically discern [the wearer's] alignment." Nothing in the spell makes mention of magically discerning alignment.

Explaination: The players want to build a mythal that has a capstone in a room protected by a forbiddance spell. The spell would still prevent access to the room except by physical means, but they were concerned about if the damage would apply. I am inclined to believe that ring would not protect against the effects of this spell, but am looking for more opinions.