May non Catholics partake of the sacrament of anointing of the sick?
The 1983 Code of Canon Law states:
§3. Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.
§4. If the danger of death is present or if, in the judgment of the diocesan bishop or conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians not having full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.
The canon clearly states that any member of the Eastern Orthodox Churches may receive the sacrament of anointing of the sick. However its a bit gray as to what other Churches or ecclesial communities these canons might apply to. It would appear that any Church with a valid line of Apostolic succession would fall under these qualifiers. Members of the Anglican communion, while not preserving valid succession, often share the same theology of the sacrament of anointing of the sick and thus might qualify. After that its difficult to ascertain who else these canons would apply to.
Section 4 applies more broadly in cases of danger of death where the nonCatholic cannot have access to their own minister.
If someone seriously ill or in danger of death professed a Catholic belief in the sacrament of anointing of the sick and requested it then many priests would anoint based on section 4 quoted above in conjunction with canon 1752:
…the salvation of souls, which must always be the supreme law in the Church, is to be kept before one’s eyes.