Is a baptized but not confirmed Catholic really a Catholic? I can't tell you how many times I've heard people say (at church also) that a baptized but unconfirmed Catholic is not really a real Catholic.

I can understand that being educated about the faith and being confirmed are important but I think it's incorrect to say that a baptized person is not really a Catholic.

Is this incorrect?

I'm looking for the official stance of the Catholic Church.
Short answer: Yes, that is incorrect, because baptism in the Catholic Church makes you Catholic

CCC 1213 


  Holy Baptism is the basis of the whole Christian life, the gateway to
  life in the Spirit (vitae spiritualis ianua), and the door which
  gives access to the other sacraments. Through Baptism we are freed
  from sin and reborn as sons of God; we become members of Christ, are
  incorporated into the Church and made sharers in her mission: "Baptism
  is the sacrament of regeneration through water in the word." 


From CCC 1227


  The baptized have "put on Christ." Through the Holy Spirit, Baptism is
  a bath that purifies, justifies, and sanctifies.  


From the Nicene Creed: 
I confess one baptism for the forgiveness of sins.  

The ideal path to receiving sacraments of initiation


The Easy answer is for children/minors: you are a Catholic when
baptized

Baptism received by a child or infant receives is the full sacrament of Baptism.  (It's not a kid's meal, it's the full serving).  During further faith formation the child is catechized and typically receives the sacraments of penance and reconciliation, and then receives the Eucharist around the age of reason (about 7 years old).  While the eventual goal is to continue catechizing and confirm the child they approach adulthood, the minor is not a partially Catholic.  Baptism has taken care of that.  (CCC 1227) 
For Adult Entering the Faith (ideal case)   

The restoration of the Catechumenate and the institution of the Rite of Christian Initiation of Adults combines the reception of all three sacraments into one rite (Baptism, Eucharist, and Confirmation) sacraments of initiation, CCC 1212-1419 typically at the Easter Vigil mass.  (Canon Law allows for other methods of reception at the discretion of the local ordinary/bishop). 


  Can.  881 It is desirable to celebrate the sacrament of confirmation
  in a church and during Mass; for a just and reasonable cause, however,
  it can be celebrated outside Mass and in any worthy place.


When this ideal path to entering into the Catholic communion is followed, the question never arises. 


What about the less than ideal path, which is where your question is coming from?

First off, let's take a look at confirmation.  What is confirmation? 


  Can.  879 The sacrament of confirmation strengthens the baptized
  and obliges them more firmly to be witnesses of Christ by word and
  deed and to spread and defend the faith. It imprints a character,
  enriches by the gift of the Holy Spirit the baptized continuing on the
  path of Christian initiation, and binds them more perfectly to the
  Church.  


Even from the canon law perspective, the person is recognized as being in the Church (being Catholic) through Baptism; Confirmation "binds them more perfectly."  

The Church does not penalize any of the faithful who were baptized as children, but who for one reason or another were not confirmed.  (CCC 1227 as above: one baptism).  What the church, both laity and clergy, are called to do is to encourage those baptized, but not yet confirmed, to undertake further faith formation and catechisis and then receive the sacrament of confirmation.  (CCC 1306-1311) 


  1306 Every baptized person not yet confirmed can and should receive
  the sacrament of Confirmation. Since Baptism, Confirmation, and
  Eucharist form a unity, it follows that "the faithful are obliged to
  receive this sacrament at the appropriate time," for without
  Confirmation and Eucharist, Baptism is certainly valid and
  efficacious, but Christian initiation remains incomplete.  


Bottom Line: even when Confirmation is delayed, the baptized Catholic is still Catholic.   



More on the "ideal" case  


  Christian Initiation
  
  1229 From the time of the apostles, becoming a Christian has been
  accomplished by a journey and initiation in several stages. This
  journey can be covered rapidly or slowly, but certain essential
  elements will always have to be present: proclamation of the Word,
  acceptance of the Gospel entailing conversion, profession of faith,
  Baptism itself, the outpouring of the Holy Spirit, and admission to
  Eucharistic communion.
  
  1230 This initiation has varied greatly through the centuries
  according to circumstances. In the first centuries of the Church,
  Christian initiation saw considerable development. A long period of
  catechumenate included a series of preparatory rites, which were
  liturgical landmarks along the path of catechumenal preparation and
  culminated in the celebration of the sacraments of Christian
  initiation.
  
  1231 Where infant Baptism has become the form in which this sacrament
  is usually celebrated, it has become a single act encapsulating the
  preparatory stages of Christian initiation in a very abridged way. By
  its very nature infant Baptism requires a post-baptismal
  catechumenate. Not only is there a need for instruction after Baptism,
  but also for the necessary flowering of baptismal grace in personal
  growth. The catechism has its proper place here.
  
  1232 The second Vatican Council restored for the Latin Church "the
  catechumenate for adults, comprising several distinct steps." The
  rites for these stages are to be found in the Rite of Christian
  Initiation of Adults (RCIA). The Council also gives permission that:
  "In mission countries, in addition to what is furnished by the
  Christian tradition, those elements of initiation rites may be
  admitted which are already in use among some peoples insofar as they
  can be adapted to the Christian ritual."
  
  1233 Today in all the rites, Latin and Eastern, the Christian
  initiation of adults begins with their entry into the catechumenate
  and reaches its culmination in a single celebration of the three
  sacraments of initiation: Baptism, Confirmation, and the Eucharist.
  In the Eastern rites the Christian initiation of infants also begins
  with Baptism followed immediately by Confirmation and the Eucharist,
  while in the Roman rite it is followed by years of catechesis before
  being completed later by Confirmation and the Eucharist, the summit of
  their Christian initiation.