Is it a scandal to give out rings and pectoral crosses to non-catholics–depends on what meaning they have to the Catholic Faith.
newadvent.org/cathen/11601a.htm
(Crux Pectoralis).
The name of the cross used by the pope, cardinals, bishops, abbots, and other prelates entitled to use the pontifical insignia. It is worn on the breast attached to a chain or silken cord, the colour differing, according to the dignity of the wearer, i.e. green, violet, or black. It is made of precious metal, ornamented, more or less, with diamonds, pearls, or similar embellishment, and contains either the relics of some saint, or a particle of the Holy Cross. It is worn over the alb during liturgical functions. The prelate should kiss the cross before putting it on his neck, and while putting it on say the prayer “Munire me digneris” (the origin of which dates back to the Middle Ages), in which he petitions God for protection against his enemies, and begs to bear in mind continually the Passion of Our Lord, and the triumphs of the confessors of the Faith. The pontifical pectoral cross is distinct from the simple cross, the use of which is often permitted by the pope to members of cathedral chapters.
newadvent.org/cathen/13059a.htm
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However, in a Decree of Pope Boniface IV (A.D. 610) we hear of monks raised to the episcopal dignity as anulo pontificali subarrhatis, while at the Fourth Council of Toledo, in 633, we are told that if a bishop has been deposed from his office, and is afterwards reinstated, he is to receive back stole, ring, and crosier (orarium, anulum et baculum). St. Isidore of Seville at about the same period couples the ring with the crosier and declares that the former is conferred as “an emblem of the pontifical dignity or of the sealing of secrets” (P.L., LXXXIII, 783). From this time forth it may be assumed that the ring was strictly speaking an episcopal ornament conferred in the rite of consecration, and that it was commonly regarded as emblematic of the betrothal of the bishop to his Church. In the eighth and ninth centuries in MSS. of the Gregorian Sacramentary and in a few early Pontificals (e.g., that attributed to Archbishop Egbert of York) we meet with various formulae for the delivery of the ring. The Gregorian form, which survives in substance to the present day, runs in these terms: “Receive the ring, that is to say the seal of faith, whereby thou, being thyself adorned with spotless faith, mayst keep unsullied the troth which thou hast pledged to the spouse of God, His holy Church.”
These two ideas–namely of the seal, indicative of discretion, and of conjugal fidelity–dominate the symbolism attaching to the ring in nearly all its liturgical uses. The latter idea was pressed so far in the case of bishops that we find ecclesiastical decrees enacting that “a bishop deserting the Church to which he was consecrated and transferring himself to another is to be held guilty of adultery and is to be visited with the same penalties as a man who, forsaking his own wife, goes to live with another woman” (Du Saussay, “Panoplia episcopalis”, 250).