Using a value that disables all replacing but enables removing the item causes removing to also be disabled. For example, if you disable replacing the helmet, it will also disable removing it, but removing should still be enabled as the value didn't mark removing as disabled.

7936 should disable replacement of every slot except for removing an item. When used, the armor stand's armor cannot be replaced, and when having an empty hand and right clicking, the armor is not removed.

/summon ArmorStand ~ ~1 ~ {DisabledSlots:7936,Equipment:[{id:stone,Count:1},{id:iron_boots,Count:1},{id:iron_leggings,Count:1},{id:iron_chestplate,Count:1},{id:iron_helmet,Count:1}],ShowArms:1b}