Well, I did ask my liberal step dad who is an attorney in TX and OK, but only for his opinion on an interpretation of the statute. Here's his reply, which I'll edit to save bandwidth:
"The Oklahoma Legislature adopted two separate and conflicting versions of the reciprocity statute (pasted below), the latter of which appears to authorize the holder of a non-Oklahoma concealed carry permit to open carry. The first version plainly does not. I would GUESS that a court in the hypothetical event of an actual prosecution would reconcile both versions by finding that, whatever other difficulties the conflicting language presents in other respects, the intent of the Oklahoma Legislature was to authorize persons with out-of-state concealed carry permits to open carry in Oklahoma.
The Okla AG and OSBI would be especially cautious about inadvertently offering unauthorized opinions in the face of the statutory conflict, and I DO NOT think you should rely upon my suggested reconciliation favorable to open carry, above. There may be some valid basis for a different outcome than I am suggesting that I (or the AG or the OSBI) might not think of. Can't know what we don't know.
-Sir"
§21-1290.26v1. Reciprocal agreement authority.
RECIPROCAL AGREEMENT AUTHORITY
The State of Oklahoma hereby recognizes any valid concealed carry weapons permit or license issued by another state, or if the state is a nonpermitting carry state, this state shall reciprocate under the permitting law of that state.
A. Any person entering this state in possession of a firearm authorized for concealed carry upon the authority and license of another state is authorized to continue to carry a concealed firearm and license in this state; provided the license from the other state remains valid. The firearm must be carried fully concealed from detection and view, and upon coming in contact with any peace officer of this state, the person must disclose the fact that he or she is in possession of a concealed firearm pursuant to a valid concealed carry weapons permit or license issued in another state.
B. Any person entering this state in possession of a firearm authorized for concealed carry upon the authority of a state that is a nonpermitted carry state and the person is in compliance with the Oklahoma Self-Defense Act, the person is authorized to carry a concealed firearm in this state. The firearm must be carried fully concealed from detection and view, and upon coming in contact with any peace officer of this state, the person must disclose the fact that he or she is in possession of a concealed firearm pursuant to the nonpermitting laws of the state in which he or she is a legal resident. The person shall present proper identification by a valid photo ID as proof that he or she is a legal resident in such a non-permitting state. The Department of Public Safety shall keep a current list of non-permitting states for law enforcement officers to confirm that a state is nonpermitting.
C. Any person who is twenty-one (21) years of age or older having a valid firearm license from another state may apply for a concealed handgun license in this state immediately upon establishing a residence in this state.
[1] Added by Laws 1996, c. 191, § 20, emerg. eff. May 16, 1996. Amended by Laws 1998, c. 286, § 7, eff. July 1, 1998; Laws 2003, c. 465, § 9, eff. July 1, 2003; Laws 2012, c. 195, § 1, eff. Nov. 1, 2012.
[2]
§21-1290.26v2. Reciprocal agreement authority.
RECIPROCAL AGREEMENT AUTHORITY
The State of Oklahoma hereby recognizes any valid concealed or unconcealed carry weapons permit or license issued by another state.
Any person entering this state in possession of a firearm authorized for concealed or unconcealed carry upon the authority and license of another state is authorized to continue to carry a concealed or unconcealed firearm and license in this state; provided the license from the other state remains valid. The firearm must either be carried unconcealed or concealed from detection and view, and upon coming in contact with any peace officer of this state, the person must disclose the fact that he or she is in possession of a concealed or unconcealed firearm pursuant to a valid concealed or unconcealed carry weapons permit or license issued in another state. Any person who is twenty-one (21) years of age or older having a valid firearm license from another state may apply for a handgun license in this state immediately upon establishing a residence in this state.