Yes, they are in communion with the Pope and Catholics are free to attend their liturgies and receive the sacraments administered by them.
Pope Francis On the occasion of the 25th anniversary of the foundation of the Priestly Fraternity of Saint Peter:
It was in a moment of great trial for the Church that the Priestly Fraternity of Saint Peter was created. In a great spirit of obedience and hope, her founders turned with confidence to the Successor of Peter in order to offer the faithful attached to the Missal of 1962 the possibility of living their faith in the full communion of the Church.
The FSSP is the Priestly Fraternity of St. Peter (in Latin Fraternitas Sacerdotalis Sancti Petri).
They offer the liturgies and sacraments of the Church as they existed before the reforms of the Second Vatican Council.
They broke from Archbishop Marcel Lefebvre’s SSPX after it was declared in schism by Pope Saint John Paul II and entered into full communion with the Pope and Church. The 1988 document Ecclesia Dei laid the groundwork for the FSSP:
To all those Catholic faithful who feel attached to some previous liturgical and disciplinary forms of the Latin tradition I wish to manifest my will to facilitate their ecclesial communion by means of the necessary measures to guarantee respect for their rightful aspirations. In this matter I ask for the support of the bishops and of all those engaged in the pastoral ministry in the Church.
- Taking account of the importance and complexity of the problems referred to in this document, by virtue of my Apostolic Authority I decree the following:
a) a Commission is instituted whose task it will be to collaborate with the bishops, with the Departments of the Roman Curia and with the circles concerned, for the purpose of facilitating full ecclesial communion of priests, seminarians, religious communities or individuals until now linked in various ways to the Fraternity founded by Mons. Lefebvre, who may wish to remain united to the Successor Peter in the Catholic Church, while preserving their spiritual and liturgical traditions, in the light of the Protocol signed on 5 May last by Cardinal Ratzinger and Mons. Lefebvre;