May divorced and "re-married" Catholics receive Holy Communion?
From Letter to the Bishops of the Catholic Church Concerning the Reception of Holy Communion by the Divorced and Remarried Members of the Faithful:3. Aware however that authentic understanding and genuine mercy are never separated from the truth(4), pastors have the duty to remind these faithful of the Church's doctrine concerning the celebration of the sacraments, in particular, the reception of the Holy Communion. In recent years, in various regions, different pastoral solutions in this area have been suggested according to which, to be sure, a general admission of divorced and remarried to Eucharistic communion would not be possible, but the divorced and remarried members of the faithful could approach Holy Communion in specific cases when they consider themselves authorised according to a judgement of conscience to do so. This would be the case, for example, when they had been abandoned completely unjustly, although they sincerely tried to save the previous marriage, or when they are convinced of the nullity of their previous marriage, although unable to demonstrate it in the external forum or when they have gone through a long period of reflexion and penance, or also when for morally valid reasons they cannot satisfy the obligation to separate.
4. [...] If the divorced are remarried civilly, they find themselves in a situation that objectively contravenes God's law. Consequently, they cannot receive Holy Communion as long as this situation persists.
The faithful who persist in such a situation may receive Holy Communion only after obtaining sacramental absolution, which may be given only "to those who, repenting of having broken the sign of the Covenant and of fidelity to Christ, are sincerely ready to undertake a way of life that is no longer in contradiction to the indissolubility of marriage. This means, in practice, that when for serious reasons, for example, for the children's upbringing, a man and a woman cannot satisfy the obligation to separate, they 'take on themselves the duty to live in complete continence, that is, by abstinence from the acts proper to married couples'". In such a case they may receive Holy Communion as long as they respect the obligation to avoid giving scandal.