1) It is a matter of doctrine (derived directly from the New Testament) that we must not receive the Eucharist when we are in a state of grave sin:
1385 To respond to this invitation we must prepare ourselves for so great and so holy a moment. St. Paul urges us to examine our conscience: "Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. Let a man examine himself, and so eat of the bread and drink of the cup. For any one who eats and drinks without discerning the body eats and drinks judgment upon himself." [1 Cor 11:27-29] Anyone conscious of a grave sin must receive the sacrament of Reconciliation before coming to communion. [from the Catechism]
2) Having sex with someone you are not married to is a grave sin.
3) The Catholic Church teaches that marriage is indissoluble. It lasts as long as both spouses are alive. From the catechism:
1664 Unity, indissolubility, and openness to fertility are essential to marriage. Polygamy is incompatible with the unity of marriage; divorce separates what God has joined together; the refusal of fertility turns married life away from its "supreme gift," the child (GS 50 § 1).
1665 The remarriage of persons divorced from a living, lawful spouse contravenes the plan and law of God as taught by Christ. They are not separated from the Church, but they cannot receive Eucharistic communion. They will lead Christian lives especially by educating their children in the faith.
This was clearly seen as a tough teaching the moment it came out of Jesus's mouth.
"I say to you, whoever divorces his wife (unless the marriage is unlawful) and marries another commits adultery.” [His] disciples said to him, “If that is the case of a man with his wife, it is better not to marry.” [Matthew 19:9-10]
4) In the eyes of the Catholic Church, therefore, someone who gets married, divorces, and then goes through a civil or Protestant marriage ceremony with a second person is still considered to be married to the first spouse. An annulment process might find reasons to believe that first marriage was not valid, in which case a new (in the eyes of the Church, a first) marriage can be entered into. But first marriages are assumed valid until proven otherwise.
5) Thus, someone who has divorced and remarried is seen by the Church as being in an adulterous relationship.
6) If someone in that situation went to confession, confessed having sex with someone to whom he was not validly married, and had a firm intention of refraining from sex with his "second wife", he would be completely free to receive communion. (If he failed in his attention and went back to having sex with his second wife, he would be unable to receive communion again unless he again confessed with an intention of refraining.)
7) If a couple which is, in the eyes of the Church, not married, intends to continue living together in an active sexual relationship as if they were married, they are in the eyes of the Church in a state of grave sin.
8) If they are in a state of grave sin, they may not receive the Eucharist: see 1) above.
Given all of that, to say that a divorced and remarried couple (unless they have decided to live together celibately) may receive communion necessarily means that you disagree with one of the following teachings of the Church:
- That someone in grave sin may not receive the Eucharist
- That having sex outside of marriage is a grave sin
- That marriage is indissoluble
Thus, there is no room for "only a change in practice" here. Any change in practice would either imply a change in doctrine, or would mean advising people to do what Paul describes as itself being a grave sin: receiving the Eucharist unworthily.