I try to think with my head, rather than my gut.
The last time we had this sort of thing happen was when the Communist Party was banned about 70 years ago (Communist Control Act of 1954), which was part and parcel of the McCarthy era. In fact, the provision of the Alaska Constitution in question is undoubtedly a remnant of that era: the Alaska Constitution was written in 1956.
While there is a certain delicious irony in a Reich winger being caught in nutcracker intended to disqualify the leftists, when I consider the after effects of that era (HUAC, black-listing, etc.) the price of the schadenfreude is too high. We don’t permit bills of attainder–we don’t sanction guilt by association. If this schmuck has done or said anything in support of the Oath Keepers’ campaign against the United States, throw him out.
His constituents should certainly question him and his associations closely in this light, but it has to be on them to throw him out if he hasn’t acted in support of the insurrectionists.