A new Responses to Doubts from the Congregation for Divine Worship clarifies Traditionis custodes’ restrictions on the traditional Latin Mass.

One particularly surprising decision requires priests to concelebrate, particularly at the holy week Chrism Mass, or permission to celebrate the Latin Mass may be denied.

Quotes from the Responsa ad Dubia:

To the proposed question:
If a Priest who has been granted the use of the Missale Romanum of 1962 does not recognise the validity and legitimacy of concelebration – refusing to concelebrate, in particular, at the Chrism Mass – can he continue to benefit from this concession?

The answer is:
Negative.

However, before revoking the concession to use the Missale Romanum of 1962, the Bishop should take care to establish a fraternal dialogue with the Priest, to ascertain that this attitude does not exclude the validity and legitimacy of the liturgical reform, the teaching of the Second Vatican Council and the Magisterium of the Supreme Pontiffs, and to accompany him towards an understanding of the value of concelebration, particularly at the Chrism Mass.

If a Latin Mass priest refuses to concelebrate at the Chrism Mass of holy week, or if he does not accept the validity and legitimacy of the Vatican II liturgical reform, or if he rejects the teaching of Vatican II and the recent Popes, then he might be denied the concession to celebrate the Latin Mass.

To the proposed question:
Does the diocesan Bishop have to be authorised by the Apostolic See to allow priests ordained after the publication of the Motu Proprio Traditionis custodes to celebrate with the Missale Romanum of 1962 (cf. Traditionis custodies, n. 4)?

The answer is:
Affirmative

In other words, the Holy See can entirely REVOKE the authority of the local Bishop to permit the Latin Mass in his diocese. He needs to be authorized by the Apostolic See in order to grant that concession. So the Bishops who most favor the Latin Mass can have their ability to support it taken away from them.

To the proposed question:
Do Deacons and instituted ministers participating in celebrations using the Missale Romanum of 1962 have to be authorised by the diocesan Bishop?

The answer is:
Affirmative.

This doesn’t seem like much of a problem, since the bishop who grants permission to the priest is probably going to allow him to choose which deacons/ministers celebrate with him.

To the proposed question:
Can a Priest who is authorised to celebrate with the Missale Romanum of 1962 and who, because of his office (Parish Priest, chaplain, etc.), also celebrates on weekdays with the Missale Romanum of the reform of the Second Vatican Council, binate using the Missale Romanum of 1962?

The answer is:
Negative.

Explanatory note.
The Parish Priest or chaplain who – in the fulfilment of his office – celebrates on weekdays with the current Missale Romanum, which is the unique expression of the lex orandi of the Roman Rite, cannot binate by celebrating with the Missale Romanum of 1962, either with a group or privately.

To the proposed question:
Can a Priest who is authorized to celebrate using the Missale Romanum of 1962 celebrate on the same day with the same Missal for another group of faithful who have received authorization?

The answer is:
Negative.

I’m not sure how the above regulation will affect the Latin Mass communities. It seems to me that many of these Latin Mass priests only say Mass in Latin.