I think the Sign of the Cross is removed as part of a inculturation process.
An article at
https://www.rcan.org/sites/default/files/files/WOW V9 N1(2).pdf explains the process of translating the Latin edition of the liturgical book, the 1969
Ordo Exsequiarum . “The second stage is the translation of the Latin into the vernacular language, which was undertaken by the International Commission for English in the Liturgy (ICEl) and with ecclesiastical approval introduced in 1970 (Rite of Funerals). The third and final stage is one of inculturation, whereby the Latin editio typica is not only translated but also adapted to the temperament and tradition of the people.”
I have a 1971 book “The Rite of Funerals” published by E.J. Dwyer which is for Australia. (It has been superseded by a 1989 edition.) It had:
“36. If the station in the home is not held, the priest goes to the entrance of the church and there greets those present, offering them his sympathy. If it is the custom, he sprinkles the body with holy water and he may say one or more of the prayers given above for the station in the home.”
It also has:
“
Mass
- After the introductory rites, the liturgy of the word is celebrated. …”
So there was nothing to suggest not having the Sign of the Cross as a normal part of the introductory rites.
It seems to me that in the inculturation process n. 36 above becomes the section “Reception at the Church” described in 131 - 136 and 158 - 161.
[The article I linked to is “A New Funeral Rite” by Charles W. Gusmer is in “Word on Worship” Newsletter of the Worship Office, Archdiocese of Newark, NJ, November/December 1989, Volume 9, No. 1.]