Please explain your understanding of
Obsequium religiosum. Here is a passage from
Lumen Gentium I have in mind:
Bishops, teaching in communion with the Roman Pontiff, are to be respected by all as witnesses to divine and Catholic truth. In matters of faith and morals, the bishops speak in the name of Christ and the faithful are to accept their teaching and adhere to it with a religious assent. This religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. His mind and will in the matter may be known either from the character of the documents, from his frequent repetition of the same doctrine, or from his manner of speaking.
to your question
canon law covers 3 stages of respect one holds for writings from the bishops
canons
Can. 750 §1. A person must believe with divine and Catholic faith all those things contained in the word of God, written or handed on, that is, in the one deposit of faith entrusted to the Church, and at the same time proposed as divinely revealed either by the solemn magisterium of the Church or by its ordinary and universal magisterium which is manifested by the common adherence of the Christian faithful under the leadership of the sacred magisterium; therefore all are bound to avoid any doctrines whatsoever contrary to them.
§2. Each and every thing which is proposed definitively by the magisterium of the Church concerning the doctrine of faith and morals, that is, each and every thing which is required to safeguard reverently and to expound faithfully the same deposit of faith, is also to be firm-ly embraced and retained; therefore, one who rejects those propositions which are to be held definitively is opposed to the doctrine of the Catholic Church.
Can. 752 Although not an assent of faith, a religious submission of the intellect and will must be given to a doctrine which the Supreme Pontiff or the college of bishops declares concerning faith or morals when they exercise the authentic magisterium, even if they do not intend to proclaim it by definitive act; therefore, the Christian faithful are to take care to avoid those things which do not agree with it.
Can. 753 Although the bishops who are in communion with the head and members of the college, whether individually or joined together in conferences of bishops or in particular councils, do not possess infallibility in teaching, they are authentic teachers and instructors of the faith for the Christian faithful entrusted to their care; the Christian faithful are bound to adhere with religious submission of mind to the authentic magisterium of their bishops.