One place to look is the incest statute, 18-6602, which says:
Persons being within the degrees of consanguinity within which
marriages are declared by law to be incestuous and void, who
intermarry with each other, or who commit fornication or adultery with
each other, are punishable by imprisonment in the state prison for a
term not to exceed life.
The relevant statute pertaining to consanguinity and marriage (32.205) states:
Marriages between parents and children, ancestors and descendants of
every degree, and between brothers and sisters of the half (1/2) as
well as the whole blood, and between uncles and nieces, or aunts and
nephews, are incestuous, and void from the beginning, whether the
relationship is legitimate or illegitimate.
A literal reading of the law with attention to the bold part tells you that the prohibition of marriage between brothers and sisters of full or half blood does not preclude marriage between blood-unrelated sibling. It does, however, not grant the same right to aunts and nephews etc. (including those by adoption), which could engender competing claims about legislative intent. It would then be relevant to look at the Washington analog of this statute, RCW 26.04.020, which prohibits marriage:
(1)(b) When the spouses are nearer of kin to each other than second
cousins, whether of the whole or half blood computing by the rules of
the civil law.
(2) It is unlawful for any person to marry his or her sibling, child,
grandchild, aunt, uncle, niece, or nephew.
Here, the blood-relation rule applies to (second) cousins and is absolute for aunts and sibling. It would seem that various legislatures had different intents, in forming these statutes.
In Oregon, ORS 106.020 prohibits marriage
When the parties thereto are first cousins or any nearer of kin to
each other, whether of the whole or half blood, whether by blood or
adoption, computing by the rules of the civil law, except that when
the parties are first cousins by adoption only, the marriage is not
prohibited or void
In this case, the Oregon law explicitly equates blood and adoption, and then could cast doubt on the concept of "whole or half blood" as actually referring to blood relationship (although, Oregon is not Idaho, or Washington).
Given the literal reading of the Idaho statutes (and without there being any clarifying case pertaining to relationship by adoption), it may take a court order to compel the county clerk to obey the law, especially if the clerk is dispensing life choice recommendations. That is especially so if the law is not clearly established.
Montana likewise restricts (40-1-401)
a marriage between an ancestor and a descendant or between a brother
and a sister, whether the relationship is by the half or the whole
blood, or between first cousins
That statute also says
Parties to a marriage prohibited under this section who cohabit after
removal of the impediment are lawfully married as of the date of the
removal of the impediment.
However, there is no obvious way to get legally unadopted, especially when the parties are adults.
An additional wrinkle is that in Idaho under 32-209, valid marriages entered into elsewhere are valid in that state
unless they violate the public policy of this state. Marriages that
violate the public policy of this state include, but are not limited
to, same-sex marriages, and marriages entered into under the laws of
another state or country with the intent to evade the prohibitions of
the marriage laws of this state.
But it is established law that same-sex marriages are legal. The bold section is clearly unconstitutional; the question then is whether if you took this to SCOTUS, they would strike down the entire statute (a number of states still have such language on their statute books, e.g. Montana still declares that marriage is between a man and a woman). At any rate, a lawyer is probably mandatory.