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As far as Pius IX the reason I put "amongst other reasons" in quotes was to show that that wasn't the ONLY reason some sede's suspect him (or throw him out completely as a valid Pope) but I didn't want to get into all that here.

My main point was that if he (Pius IX) WAS a Freemason before his election then he would have been automatically excommunicated before his election and never would have had a valid Papacy. 

Most of the Vacancy Pushers won't consider even the Vatican I Council as legitimate and throw out all Popes as Anti-Popes past that so Pius XII's decisions will mean nothing and if Pius XII was a Freemason then of course he would lift excommunications as impediments but if he was a Freemason he wouldn't have held the office at all.

I don't know of any sedevacantist who questions Pius IX ... except one guy I ran into once (now deceased), but his reasoning was rather bizarre and not worth going into here.  In any case, I would have to imagine that the same reasoning would apply in the hypothetical scenario as would with the notion of heresy disqualifying a legitimate pope, i.e. that his excommunication would have to be MANIFEST in order for him to have been excluded from the papacy.  If someone had occurred one of those ipso facto excommunications, and yet it was unknown to anyone else, perhaps not even to the perpetrator himself, that certainly would not preclude the legitimacy of a papal election.  As per St. Robert Bellarmine, excommunication would render a pope illegitimate on the grounds that it was one way in which someone could be severed of membership in the Church, but membership (or lack thereof) must be manifest.

But, as 2Vermont points out, the core issue really isn't about the persons involved, but rather about the fact that it's not possible for legitimate popes to wreck the Church as these V2 papal claimants have.  As to why they're illegitimate, that can be the subject of debate (and I myself hold to the Siri theory).

I don't know of any sedevacantist who questions Pius IX ... except one guy I ran into once (now deceased), but his reasoning was rather bizarre and not worth going into here.  In any case, I would have to imagine that the same reasoning would apply in the hypothetical scenario as would with the notion of heresy disqualifying a legitimate pope, i.e. that his excommunication would have to be MANIFEST in order for him to have been excluded from the papacy.  If someone had occurred one of those ipso facto excommunications, and yet it was unknown to anyone else, perhaps not even to the perpetrator himself, that certainly would not preclude the legitimacy of a papal election.  As per St. Robert Bellarmine, excommunication would render a pope illegitimate on the grounds that it was one way in which someone could be severed of membership in the Church, but membership (or lack thereof) must be manifest.

But, as 2Vermont points out, the core issue really isn't about the persons involved, but rather about the fact that it's not possible for legitimate popes to wreck the Church as these V2 papal claimants have.  As to why they're illegitimate, that can be the subject of debate (and I myself hold to the Siri theory).

But epiphany says my statement has no value!