The Church teaches clearly: Anyone who objectively lives in a continuing, irregular union and does not live in continence cannot receive Communion as long as this situation persists.
Foundations:
John Paul II, Familiaris Consortio 84,
Benedict XVI, Sacramentum Caritatis 29
CIC can. 915 (Persons who obstinately persist in manifest grave sin are not to be admitted to Communion)
This remains unchanged, applies universally in the Church, and is an expression of the sacramental order.
John Paul II, Familiaris Consortio (1981), No. 84
The Church, however, reaffirms her practice, based on Sacred Scripture, of not admitting divorced and remarried persons to Eucharistic Communion. They cannot be admitted: They find themselves in a situation which objectively contravenes that union of love between Christ and the Church signified and made present by the Eucharist. Furthermore, there is another specific pastoral reason: If these people were admitted to the Eucharist, the faithful would be led into error and confusion regarding the Church’s teaching about the indissolubility of marriage.
Reconciliation in the sacrament of Penance—which opens the way to the Eucharist—can only be granted to those who, repenting, are sincerely willing to undertake a way of life in full conformity with the teaching of Christ, and who commit themselves to living in complete continence, that is, to abstain from acts proper to married couples.
This applies not only to the Church, but finds its inner justification in the relationship between the Eucharist and marriage. The Eucharist is the sacrament of the Church’s unity, and marriage—being an image of this unity—forms an indissoluble community.
(Familiaris Consortio, No. 84)
Benedict XVI, Sacramentum Caritatis (2007), No. 29
The Synod Fathers have drawn attention to the pastoral problem of those faithful who are divorced and civilly remarried. The Church has a loving concern for them and encourages them to participate in the life of the Church: They should attend Holy Mass, listen to the Word of God, take part in Eucharistic adoration, persevere in prayer, and perform works of charity.
Nevertheless, the Synod confirmed the Church’s practice of upholding the doctrine of the indissolubility of marriage, founded on Sacred Scripture (cf. Mk 10:2–12).
Divorced persons who have entered a new union cannot receive the sacraments as long as this situation persists and as long as they do not live as brother and sister, that is, in complete continence.
This is not a punishment or exclusion, but an expression of the objective situation which is in contradiction to the sacrament of marriage. At the same time, pastors should take special care with love to ensure that these faithful do not feel separated from the Church, but—so far as possible—remain integrated into the life of the community.
The Church is called to do everything possible to accompany these people, to serve them, and to help them seek the path of truth and reconciliation.
(Sacramentum Caritatis, No. 29)
CIC can. 915 – Text
Those who have been excommunicated or interdicted after the imposition or declaration of the penalty and others who obstinately persist in manifest grave sin are not to be admitted to Holy Communion.