There has been quite a bit of controversy over what is becoming known as 'modern Catholicism' (post-Vatican II) and 'traditional Catholicism' (pre-Vatin II). 'Modern Catholicism' thought generally holds that divorcees who have not had their marriages annulled and are in another marriage can still receive Communion, so long as they repent. 'Traditional Catholicism' thought, to my understanding, generally holds that divorcees who have not had their marriages annulled and are in another marriage cannot receive Communion since they are still in a state of sin so long as they are neglecting their previous marriage that is not annulled. Assuming the traditional Catholic view to be true, what would be the solution to this problem for the remarried divorcee? Would the traditionalist Catholic suggest that the divorcee divorce the person that they are currently married to (in which case I'm assuming that marriage would be annulled)? And if so, would the person then be obligated to return to the marriage they left (which seems very improbable and unrealistic)? If it is a continual sin to be with another person while your previous marriage is still considered valid, in what way should the more complicated situations of divorce without annulment be evaded?
Let's start with a discussion of what the situation is, as the Church traditionally has seen and taught it:
The official teaching of the Church is that civil divorce is usually immoral in itself, but may be morally tolerable under certain circumstances:
If civil divorce remains the only possible way of ensuring certain legal rights, the care of the children, or the protection of inheritance, it can be tolerated and does not constitute a moral offense.
(Catechism of the Catholic Church, paragraph 2383)
And a Catholic who is "the innocent victim of a divorce decreed by civil law" (Catechism paragraph 2386) is not committing a moral offense.
However, even in these two cases, the Church teaches that the civil divorce does not in itself end the marriage before God - indeed, that is impossible if the marriage is valid:
A marriage that is ratum et consummatum [that is, validly constituted, and subsequently consummated] can be dissolved by no human power and by no cause, except death.
(Code of Canon Law, Canon 1141)
That being the case, the question of whether the couple are "still married"—that is, whether they were validly married in the first place—must be investigated beyond determination of their divorced status. The Church will presume, in the absence of evidence to the contrary, that the couple are indeed still married, because this is how the Church works: it assumes a marriage is valid until it can demonstrate it to be invalid:
In a doubtful matter marriage enjoys the favor of the law.
(Code of Canon Law, canon 1150)
Thus, the traditional Catholic view is that a divorced couple who have not obtained a decree of nullity (an annulment) are still considered married.
This is not a problem in itself; but if the couple is remarried (civilly—they wouldn't be able to be remarried in the Church), the Church considers them to be committing adultery:
If a husband, separated from his wife, approaches another woman, he is an adulterer because he makes that woman commit adultery; and the woman who lives with him is an adulteress, because she has drawn another’s husband to herself.
(Catechism, paragraph 2384, quoting St. Basil, Moralia paragraph 73)
Adultery being a quite serious sin, the Church teaches that the civilly remarried couple are not fit to receive the Eucharist:
If the divorced are remarried civilly, they find themselves in a situation that objectively contravenes God’s law. Consequently, they cannot receive Eucharistic communion as long as this situation persists.
(Catechism paragraph 1650)
The Catechism of the Catholic Church does offer some suggestion about what to do in such a case:
Reconciliation through the sacrament of Penance can be granted only to those who have repented for having violated the sign of the covenant and of fidelity to Christ, and who are committed to living in complete continence. ... They should be encouraged to listen to the Word of God, to attend the Sacrifice of the Mass, to persevere in prayer, to contribute to works of charity and to community efforts for justice, to bring up their children in the Christian faith, to cultivate the spirit and practice of penance and thus implore, day by day, God’s grace.
(Catechism para. 1650–51; the second sentence is quoted from Familiaris Consortio)
It is not specified what "in complete continence" means; it could mean that the remarried couple is to separate, or at least that they are to live together without sexual or romantic activity of any sort—either of which would be no doubt rough on their relationship, and certainly on any children of their union. The Church nowhere seems to teach that someone must go back to their previous marriage, though perhaps that might be suggested by individuals whom the couples could consult for guidance. It appears to prefer that, since the civilly divorced couple have given an indication that they are unable to live together, they should live separately and in celibacy—either with or without the company of their civilly-remarried spouse.
This is no doubt "a hard saying" (cf John 6:60); many in such a situation understandably feel that the Church is abandoning them. Nevertheless, the Church currently teaches that this is the only way available to insist on (a) the holiness of the Eucharist and (b) the lifelong nature of marriage. Those who are searching for a different approach do so out of pastoral feelings for Catholics affected by the situation, which they are trying to reconcile with the formal teachings of the Church.
The problem isn't the divorce, but the remarriage. If you simply get a divorce for a good reason, you are not in state of sin - although the divorce itself is a mortal sin.
The real problem is remarriage. Modernist Catholics say divorcees who have not had annullment and have another partner can receive communion, but it has never been (and it never will be) the teaching of the Church, because it is against Our Lord's law.
The teaching of the Church is: Marriage is indissoluble. If someone gets divorced, there are not much options...
If the person is not "remarried", the person must remain on celibacy until the partner dies (or until death)
If the person is "remarried", or it leaves the "new partner" or they'll live like "brothers", with absolutely no intimacy, as it would be adultery.
If else, the person lives in state of mortal sin, thus cannot receive the sacraments (Not even the Reconciliation, if there is no will to abandon the "new partner"
There are no "gray areas".
In September 2015 Pope Francis issued a motu proprio Mitis iudex dominus Jesus which bears on this question. It does not change the need for a declaration of nullity as regards the prior marriage, but it does streamline the process, especially if the original marriage is invalid because of a lack of form. A baptized Catholic must follow proper form--the marriage must be witnessed by a Catholic priest or deacon or the Catholics party(s) must have been granted a dispensation for the marriage to be valid. Metropolitan Tribunal, Archdiocese of Saint Paul and Minneapolis. According to Art. 6, Can. 1688 of the motu proprio;
After receiving a petition proposed according to the norm of can. 1677, the diocesan bishop or the judicial vicar or a judge designated by him can declare the nullity of a marriage by sentence if a document subject to no contradiction or exception clearly establishes the existence of a diriment impediment or a defect of legitimate form, provided that it is equally certain that no dispensation was given, or establishes the lack of a valid mandate of a proxy. In these cases, the formalities of the ordinary process are omitted except for the citation of the parties and the intervention of the defender of the bond.