Pope Pius XII again reiterates traditional teaching on the reception of the Eucharist: a priest must, lay people do not have to partake.
115. Now it cannot be over-emphasized that the eucharistic sacrifice of its very nature is the unbloody immolation of the divine Victim, which is made manifest in a mystical manner by the separation of the sacred species and by their oblation to the eternal Father. Holy communion pertains to the integrity of the Mass and to the partaking of the august sacrament; but while it is obligatory for the priest who says the Mass, it is only something earnestly recommended to the faithful.
That said, the Church is interested in the spiritual vitality of all the faithful:
116. The Church, as the teacher of truth, strives by every means in her power to safeguard the integrity of the Catholic faith, and like a mother solicitous for the welfare of her children, she exhorts them most earnestly to partake fervently and frequently of the richest treasure of our religion.
Touching on a communion of desire:
117. She wishes in the first place that Christians – especially when they cannot easily receive holy communion – should do so at least by desire, so that with renewed faith, reverence, humility and complete trust in the goodness of the divine Redeemer, they may be united to Him in the spirit of the most ardent charity.
Union is possible through caritas, a concept which extends to those outside of union with Rome. A pretty far leap from lumping the children of the Reformation or 1054AD with heretics and schismatics.