Leaving aside the highly uncritical nature of these claims, what would the effect be if they were true? What if indeed Jesus did not bring anything new in the religious agora? By my lights, the effect would be quite small, or rather, quite illuminating in the opposite direction the critics intend.
Christ did not come to invent a new thing, but to redeem all old things (though this redemption in some cases means judging end expunging some things). Objecting that Christ did not invent anything conceptually new is as irrelevant, theologically, as claiming He did not invent any new chemical elements or fashion trends. He did not invent a new biology for humans either; He "copied" the old one to redeem it. He came to redeem the entire creation, to redirect it to its original telos by a singular and authentic act of human consecration to the Ultimate, the Father of lights. In a key respect, then, Christ had to be redundant. For as the Fathers stated time and again, "what is not assumed, is not healed." It was precisely by "mimicking" and assuming (incorporating) older ways of thought (and speech and even behavior) that Christ assumed them into his perfect act of consecration.
To tweak a biblical proverb, "There is nothing new in the Son". There need not be anything utterly new because the point of the Incarnation was not didactic novelty but saving renewal. Christ emptied Himself into the categories and limitations of the creation in order to fill them from within. Adding new layers to the creation would only create barriers, calluses as it were, between His saving Incarnation and fallen creatures. If the Son did not assume temporality, He could not redeem temporal beings. If the Son did not assume corporeality, He could not redeem corporeal beings. If He did not assume language, He could not redeem speaking agents. And so forth. The specific point for this post is that if He did not assume, say, Stoic truths or rabbinic precedents, then He could not redeem people attached to those truths. Much the same holds for other religious parallels.
This is the great and shocking truth of recapitulatio (or anakephailosis), found most prominently in St. Irenaeus: all things are drawn from their roots back to their true head, the Father, in Christ, the Head of the Church. The biblical roots of the doctrine are clear in a passage like Ephesians 1:10:
In the dispensation of the fulness of times, to re-establish all things in Christ, that are in heaven and on earth, in him. (plhrwmatoV twn kairwn anakefalaiwsasqai ta panta en tw cristw).In fuller form, as St. Gregory Nazianzen said,
If anyone has put his trust in Him as a Man without a human mind, he is really bereft of mind, and quite unworthy of salvation. For that which He has not assumed He has not healed; but that which is united to His Godhead is also saved. If only half Adam fell, then that which Christ assumes and saves may be half also; but if the whole of his nature fell, it must be united to the whole nature of Him that was begotten, and so be saved as a whole. Let them not, then, begrudge us our complete salvation, or clothe the Saviour only with bones and nerves and the portraiture of humanity.
The ascended Christ can, by the infused power of the Holy Spirit in "earthen vessels" continue to assume things "apostolically" (vicariously), by His Body the Church, so His "assumptive" powers are not limited to His pre-glorified, localized person. This is the principle behind why the Church has such a stunning (if not always uncontroversial) history of appropriating cultures. The Church endures in every age in order to assume redeemable treasures from every age, so they may be reconstituted for the end of the ages at the final heavenly banquet. The paradox is that even when it tries to incorporate "old leaven", the Church is relentlessly novel in its recreation of the old ways. As John Zizioulas argues in Being as Communion, the Church virtually created the concept of "person" by appropriating and transforming -- redirecting -- pagan concepts like persona, hypostasis, substantia, ousios, etc. (Much the same can be gleaned from Pelikan's Christianity and Classical Culture, among a number of works in the same vein.) This unwittingly regenerative power of the Church is especially evident at Christmastime, when whole swaths of pagan fabric have been assumed, washed, refitted, restitched and worn anew in honor of Christ the King.