Explicitly desires to be part of God's one true Church.
Explicit desire is not a magical formula. Study and examination of the Church are necessary even for lifelong professors of the Faith.
Explicitly desires to do all that God requires of them.
Again, nobody gets a pass. The savage pagan in the jungle can have that excuse that they didn't know any better and were just trying to 'love God', but that doesn't wash in the modern world.
Explicitly desires to be subject to the Roman Pontiff.
You've got to be kidding. Anyone who does even the littlest bit of reading of a NEWSPAPER, let alone a website devoted to the traditional Faith, can tell you what it means to be subject to the Roman Pontiff.
Explicitly receives a baptism with water with the desire to join said Church.
THAT gives one entrance into the Church regardless of the other errors, but we must go on to address the other points you've raised; this one doesn't stand on its own, and in the teaching of the Magisterium and of Christ and the Apostles, it never has.
Believes all tenets of the creed.
Again, important, but not all-sufficient, not even close.
How can someone say that person is not a Catholic and part of God's Church??
One CAN'T say that a validly-baptized person is not a part of the Church; that said, however, there are these other factors which you've raised and which I think a LOT of Conciliar people like to conveniently forget, especially in the case of their 'separated brethren'.
In my opinion Vatican 2 Catholics are deprived of confession and several other sacraments and their catechism has many errors.
When a person is baptized, they are in the state of sanctifying grace. When they confess validly, they are absolved of the penalties of their sins. When a person receives Holy Communion, they are likewise endued with many, many graces that are simply not available otherwise.
Now, we know that a person can be validly baptized even by a Protestant layperson. IF, however, a person is baptized and then attends a Novus Ordo congregation (presided over by a Novus minister and not a priest), they are being offered invalid confession, which leaves them in sin. They are being offered invalid wafers instead of the Eucharist, which not only leaves them in sin, but causes them to be guilty of sacrilege, because they venerate and worship a cracker rather than Our Lord, Present sacramentally in the Sacrifice of the Altar.
When we are speaking hypothetically about a person who was born, baptized and raised in the Novus Ordo, we are talking about a person that was likely to have been validly baptized (at least we ASSUME so; I am sure there are Novus Ordo ministers out there who have changed the entire rite of baptism by now in their 'faith communities'). Baptism notwithstanding, the person is in spiritual darkness and devoid of the sanctifying grace that God has provided IN the valid Sacraments. Such a person needs to be rescued from a perverse and distorted usurpation of the authority of Holy Church. It may not be their personal FAULT that they are in such a position, but they certainly cannot plead IGNORANCE. Ignorance is for those that don't know that there's a Faith to BE studied; even a Novus 'catholic' should be looking into their Church and what the Novus con-men have done to it.
Many in my opinion probably are not Catholic based on there [sic] beliefs and actions.
Many, indeed, like Bugnini, Roncalli, Montini, Luciani, Wojtyla, Ratzinger... the list goes on.
I value your input, and I thank you for wanting to open up sincere discussion. Discussion, however, cannot change incontrovertible facts. Those include the invalidity of any new Missals after the one promulgated by Pope St. Pius V, the invalidity of all-vernacular liturgies, the manifest heresies of the aforementioned usurpers and the GRAVE and IMMUTABLE responsibility of EVERY professing Catholic to know their Church and their Faith.
The existence of the Novus Ordo is at LEAST as likely because of the willful ignorance of the pew-sitters as it is because of the machinations of the Conciliar criminals.
St. John Vianney, pray for us.
Immaculate Heart of Mary, triumph soon.
Sacred Heart of Jesus, have mercy on us.