No bishop would object and thus there would be no need to seek permission from one's bishop.
The only change Pope Francis has made is to make sure that the candles and crucifix do not become like a wall hiding the priest and the elements on the altar, all of which have a sacramental symbolic importance as well.
The congregation and priest facing the crucifix even while facing each other makes the crucifix the symbolic point of facing eastward toward Calvary! Keep in mind, that in most parish churches, the placement of the altar is not eastward facing when the priest and laity face the same direction, it is a symbolic gesture as is placing the crucifix dead center on the altar when priest and laity face each other. Both are symbolic of facing eastward toward Calvary and the New Jerusalem.
This is what I found on the Vatican website which remains there to this day:
OFFICE FOR THE LITURGICAL CELEBRATIONS
OF THE SUPREME PONTIFF
The Crucifix at the Center of the Altar
The liturgy is the celebration of the mystery of Christ and in particular his paschal mystery. Through the exercise of the priestly office of Jesus Christ, the liturgy manifests in signs and brings about the sanctification of humankind. The public worship which is due to God is offered by the Mystical Body of Christ, that is, by its head and by its members. (n. 218)From this definition, one understands that Christ the Eternal High Priest and the Paschal Mystery of his Passion, Death and Resurrection are at the center of the liturgical action of the Church. The liturgy must be the celebrated transparency of this theological truth. For many centuries, the sign chosen by the Church to orient the heart and the body during the liturgy has been the depiction of the Crucified Jesus.
The centrality of the crucifix in the celebration of divine worship was more evident in the past, when the normative custom was that both priests and faithful would turn and face the crucifix during the eucharistic celebration. The cross was placed in the center above the altar, which in turn was attached to the wall, according to the norm. For the present custom of celebrating the Eucharist “facing the people,” often the crucifix is located to the side of the altar, thus losing its central position.
The cross is the unique sacrifice of Christ, the “one mediator between God and men” (1 Tim 2:5). But because in his incarnate divine person he has in some way united himself to every man, “the possibility of being made partners, in a way known to God, in the paschal mystery” is offered to all men (Gaudium et Spes, n. 22). He calls his disciples to “take up [their] cross and follow [him]” (Mt 16:24), for “Christ also suffered for [us], leaving [us] an example so that [we] should follow in his steps” (1 Pt 2:21). In fact, Jesus desires to associate with his redeeming sacrifice those who were to be its first beneficiaries (cf. Mk 10:39; Jn 21:18-19; Col 1:24). This is achieved supremely in the case of his mother, who was associated more intimately than any other person in the mystery of his redemptive suffering (cf. Lk 2:35). “Apart from the cross, there is no other ladder by which we may get to heaven” (St. Rose of Lima, in P. Hansen, Vita Mirabilis [Louvain, 1668]).
1The Spirit of the Liturgy (San Francisco: Ignatius Press, 2000), 83.