Actually, the vast majority of SVs are rather devoted to OL of Fatima.  The CMRI has had a Fatima Conference for over 40 years, as just one example.

IMO, trads of ALL stripes get into trouble when they start excluding from the Church those with whom they disagree about the present crisis.  Would that this phenomenon were limited to just SPs or SVs; it is not.

How could the Pope consecrate Russia, for example, if we don't have a Pope?

Perhaps this is one of the concrete ways in which sedevacantism conflicts with Catholicism?

Perhaps the failure to consecrate Russia is one of the ways we know the V2 and post-V2 popes are impostors?

IMO, that is at least as "concrete", if not more so, than the point you have chosen to mention.

Did BXV know about the demand?  Did Pius XI?  When was it made known to the Pontiff?  It would seem Pius XII knew about it, but did not follow Our Lady's directions.

I personally think Pope Pius XII was the suffering Holy Father, of whom Our Lady spoke. He might have been afraid to consecrate Russia because of what the reaction of his enemies would be if he did. I believe he even uttered his worries over the messages of Fatima, complaining that he saw all around him, enemies who wanted to tear down the sacred chapel, change the theology and liturgy of the Church, so much that he dared to say that there would come a time when 'people would seek the red lamp in vain' (of the tabernacle).

Methinks he was the 'suffering Pontiff'.

I do believe the Church will have a valid Pope again, who will make the consecration and restore the traditions and rights of the Church.

Even Richard Dawkins, in his The God Delusion, admits that he has "no natural explanation" for the events that occurred just northeast of Fatima, Portugal on October 13, 1917.  What is there not to accept about it?  It's kind of like saying that one believes in the existence of the Sun but not the Moon.

I'm not saying I reject Fatima or that a person should reject Fatima, I'm just stating that it isn't non-Catholic to do so.

Until I joined CathInfo, I was not aware that there were any sedevacantists that rejected Fatima.  I have spoken to quite a number of sedevacantists, read the writings of quite a few sedevacantists, and I have never heard or read of any of them rejecting Fatima as a true apparition of the Blessed Virgin Mary.  (I admit that Fatima is not always a topic of conversation.)  All of the sedevacantists I personally know pray that "Fatima Prayer" (i.e., "O my Jesus...") after the Gloria when praying the Rosary.

On the other hand, I know a few Conciliar Catholics (both ones who ordinarily attend a traditional indult Mass and ones who exclusively attend the Novus Ordo) who reject Fatima, accept the "Third Secret" released by Cardinal Ratzinger, and the official explanation that Sister Lucia may have just made up the whole thing from forgotten memories of stories she had heard or read.  And one of these believes Medjugorje is clearly a true apparition (largely, I think, because one of the messages said John Paul 2 was "her pope" and many of her messages mirror Conciliar doctrines).

These are simply my experiences.  I would not presume to paint all Conciliar Catholics with rejecting Fatima because I know Conciliar Catholics who reject Fatima.  I think it unfair to paint all sedevacantists with particular beliefs based upon what a few particular sedevacantists say they believe.

We need to keep in mind that the term, "sedevacant" was coined only a few years ago.  This is why we find no references to "sedevacantists" a hundred years ago.  We likewise find no references to "dinosaurs" prior to 1841.  It's not that no one believed in dinosaurs before then, it's that the word was invented in that year.

For better or worse, the word "sedevacantist" means nothing more or less than a person who believes that Benedict 16 is not a valid claimant to the See of Peter.  Some sedevacantists eschew the term, but this is the commonly accepted term.  Sedevacantism is not a movement, a group, a set of doctrines, or anything other than the recognition of the fact that Benedict 16 is not a valid claimant to the papacy.

Fatima has nothing to do with whether one might or might not be a sedevacanist.

The approved Fatima apparition has very little content besides "Repent."

It is the secrets that are controversial.  Your reaction to them probably depends on your worldview.  

My problem with the "consecration of Russia" idea, it is easy for me to figure out, comes from too much exposure to Catholics who think America is the greatest country ever and spend too much time living in a Cold War movie in their heads, demonizing Russia.  I have seen the Fatima secret used in order to increase blind patriotism.

Then TKGS talks about Vatican II people who find the Fatima secrets too doom-laden.

I know of others who aren't sedevacantist because Mary said the Pope would have much to suffer, therefore we must still have a Pope... ( Did Mary say when and who this Pope would be, how they do they know he didn't die a long time ago? )

It's really a Rohrschach blot, these secrets.  That is another aspect that worried me, that they were causing more confusion.  But it's a chicken or the egg question -- is it the Fatima secrets that caused confusion, or is it people slapping their own prejudices onto the Fatima secrets that caused confusion?  

Today, I made great progress towards believing, the only aspect that still troubles me is the second secret being released subsequently to the war that it was supposed to prevent, if Mary's words were heeded.  And it wasn't a cover-up, from what I can tell, but that is when Lucia wrote it down.