Saying the propers is foreseen by Pius XII's permission of the dialogue Mass.

Please provide docuмentation for this assertion of yours. Also, explain why no one else seems to have drawn the conclusion you do.

"A final method of participation, and the most perfect form, is for the congregation to make the liturgical responses to the prayers of the priest, thus holding a sort of dialogue with him, and reciting aloud the parts which properly belong to them.
There are four degrees or stages of this participation:
a) First, the congregation may make the easier liturgical responses to the prayers of the priest: Amen; Et cuм spiritu tuo; Deo gratias; Gloria tibi Domine; Laus tibi, Christe; Habemus ad Dominum; Dignum et justum est; Sed libera nos a malo;
b) Secondly, the congregation may also say prayers, which, according to the rubrics, are said by the server, including the Confiteor, and the triple Domine non sum dignus before the faithful receive Holy Communion;
c) Thirdly, the congregation may say aloud with the celebrant parts of the Ordinary of the Mass: Gloria in excelsis Deo; Credo; Sanctus-Benedictus; Agnus Dei;
d) Fourthly, the congregation may also recite with the priest parts of the Proper of the Mass: Introit, Gradual, Offertory, Communion. Only more advanced groups who have been well trained will be able to participate with becoming dignity in this manner.
32. Since the Pater Noster is a fitting, and ancient prayer of preparation for Communion, the entire congregation may recite this prayer in unison with the priest in low Masses; the Amen at the end is to be said by all. This is to be done only in Latin, never in the vernacular."
https://adoremus.org/1958/09/instruction-on-sacred-music/

There are actually 3 approved variants of the dialogue/conversation Mass.

We need variety, man!

It set the table for the total destruction of liturgical unity in the Roman rite in what would revolve into the Novus Ordo.

Decent Wiki article:

https://en.m.wikipedia.org/wiki/Dialogue_Mass

Or 4 approved varieties:

“The 1958 docuмent Musica sacra divides dialogue Masses into four degrees of outward, vocal expression.  In a nutshell,

The congregation makes the shorter responses such as the Amen, Deo gratias, Et cuм spiritu tuo along with the servers.

Same as above but adding all the responses of the servers, including the prayers at the foot of the altar, Second Confiteor where used, etc..

Same as above adding the Ordinary (e.g. Kyrie, Gloria, Credo, etc.) together with the priest and/or choir.

Same as above adding even the Propers (Introit, etc.) with the priest and/or choir.”

https://wdtprs.com/2015/03/ask-father-extraordinary-form-dialogue-masses/

No, I have never been to his Mass which seems unique. I went to St. Agnes a few times over a decade ago, and I remember there being a dialogue Mass (I think as it was so long ago). I don't know the name of the priests who were there. They tell me that St. Agnes no longer has the traditional Mass, but now they have the Novus Ordo in Latin. The rumor is that it is now run by Opus Dei and they hate the traditional Mass. Don't know if that is true, but that is what people are saying. And the other Indult I have been to is Holy Innocents with Fr. Miara as pastor which was not a dialogue Mass. The independent chapel is Our Lady of La Salette in Bayside and they had a dialogue Mass also.

Father Miara is a very fine man, perhaps even a saintly man. He is completely conscious of the rot within newChurch and is doing what he can to combat it.

"A final method of participation, and the most perfect form, is for the congregation to make the liturgical responses to the prayers of the priest, thus holding a sort of dialogue with him, and reciting aloud the parts which properly belong to them.
There are four degrees or stages of this participation:
a) First, the congregation may make the easier liturgical responses to the prayers of the priest: Amen; Et cuм spiritu tuo; Deo gratias; Gloria tibi Domine; Laus tibi, Christe; Habemus ad Dominum; Dignum et justum est; Sed libera nos a malo;
b) Secondly, the congregation may also say prayers, which, according to the rubrics, are said by the server, including the Confiteor, and the triple Domine non sum dignus before the faithful receive Holy Communion;
c) Thirdly, the congregation may say aloud with the celebrant parts of the Ordinary of the Mass: Gloria in excelsis Deo; Credo; Sanctus-Benedictus; Agnus Dei;
d) Fourthly, the congregation may also recite with the priest parts of the Proper of the Mass: Introit, Gradual, Offertory, Communion. Only more advanced groups who have been well trained will be able to participate with becoming dignity in this manner.
32. Since the Pater Noster is a fitting, and ancient prayer of preparation for Communion, the entire congregation may recite this prayer in unison with the priest in low Masses; the Amen at the end is to be said by all. This is to be done only in Latin, never in the vernacular."
https://adoremus.org/1958/09/instruction-on-sacred-music/

This all stems from De musica sacra, a docuмent written in toto by Bugnini. There is nothing here remotely congruent with Tradition. You might just as well quote Satan directly.

Again, thank you—and as regards De musica sacra, just so. The fact remains that Father Villa is the only priest I have ever encountered who treats the last option as something other than a Bugniniesque obscenity best left to the celebration of the Novus Ordo party-time excuse for the mass. Wikipedia's implication that congregational yakking during the Proper antedated 1958 is either stupid or dishonest. Neither adjective seems out of place, of course, when Wikipedia is being discussed.

I’ve never seen the 4th option done either.  It’s like one step short of having the faithful concelebrate.
I can’t stand the dialogue Mass in any form, and refuse to attend one.

I can’t stand the dialogue Mass in any form, and refuse to attend one.

I have as little use for it as you do, Sean, as I have said here for years. Unfortunately, there have been many occasions when I have attended such a Mass because my only other option was to stay at home. I do not criticize anyone who, in a similar situation, makes the contrary choice, but I myself am uncomfortable with staying at home except as a last resort, especially as I must frequently miss Sunday Mass because of ill health.

What parish is doing option 4? At that point, it's the Novus Ordo with window dressing.