
   When an alleged private revelation attracts sufficient attention,
   the Church may investigate it.  If the investigation indicates a
   likelihood that the alleged private revelation is in fact from God,
   it will be approved.  That means that it can be preached in the
   Church.  However, it is still true that no one is required to
   believe that it came from God.  A Catholic is free to deny the
   authenticity of even the most well attested and strongly approved
   private revelations, such as those at Fatima and Lourdes.  (I
   suspect that few if any Catholics do reject Fatima and Lourdes, but
   if any do their rejection of them does not mean they are not
   orthodox Catholics in good standing.)

It may be a bit much to say that a Catholic is free to deny what
happened at Fatima.  That's a bit strong, it is sort of like saying
that a Catholic is free to deny that Hong Kong exists.  What a
Catholic *is* free to do is to deny the truth of Fatima, without being
called a heretic.  You can be labeled other things for such an
offense, but not a heretic.

Theologians make a basic distinction as far as the degree of assent
one must give to events like Fatima and Lourdes.  Things revealed by
God through Jesus Christ or His Apostles must be given the assent due
to a revelation of God: total and unswerving.  Fatima and Lourdes
demand our assent as much as any other well-attested event in human
history.  Perhaps a bit more, given the approval of the Church.

"Approval" of an apparition by the Church principally means that
whatever happened was in harmony with the Catholic Faith.

I personally think of private revelations as our Lord's way of telling
us what to do at particular periods in history.  He gave us all the
doctrines, etc., 2000 years ago, but we can always use some help in
knowing how exactly to apply what He gave us.

Catholic devotion to the Sacred Heart was a result of a series of
apparitions to St. Margaret Mary Alacoque, for example.  The problem
at the time was extreme moral rigorism that was turning our Lord into
someone without a heart.