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Well, the first part of the question, of course, you made the profession of faith, the Catholic faith. You became Catholic, even though the Society of Pius X does not yet have the canonical structure; they are valid priests. They even received from Pope Francis the faculties for confession. Therefore, they are fully Catholic because they recognize the Pope. They pray for the Pope and for the local bishop.
But because of the emergency crisis of the Church, of the faith within the Church, and even the crisis which has reached the Holy See and the Vatican, with the infiltration of modernism and the promotion of liberal doctrinal ideas, as we are now seeing in our day, there is a reason for the faithful to participate even in the Holy Masses of the Society of Pius X because they are in no way schismatics.
A schismatic will never pray for the Pope. A schismatic will never recognize the local bishop in the official prayer of the Church. A schismatic will never profess the dogma of faith, the primacy of the Pope, the infallibility of the Pope, and all the dogmas which the Church proclaimed. And they do so. They make the same profession of faith as the Church always did until the Second Vatican Council.
Even after the Second Vatican Council, the profession of faith which the Society of Pius X uses was still valid until 1967, two years after the Second Vatican Council. This is the same profession of faith used by the Society of Pius X and by those people who join them.
Follow-up Question: Do Catholics fulfill their Sunday obligation by attending Mass at an SSPX chapel, or should attending SSPX chapels be avoided?
And so, regarding the second question on the Holy Mass, the obligation is connected with the third commandment of God. We have to observe the third commandment of God, which obliges us by divine law to sanctify the holy day of Sunday. But the concrete manner of applying this is then a Church law. So the Church law obliges us to attend Holy Mass on Sundays unless there are serious reasons for exception.
Therefore, we must distinguish this properly. When people attend Holy Mass at a chapel of the Society of Pius X, they surely fulfill the divine commandment of the third commandment. The question is whether they also fulfill the Church commandment, the human canonical commandment to attend Holy Mass on Sundays.
This is sometimes discussed because those who have a very narrow legalistic view deny it and say they must go to a community recognized by the Holy See. I think that they do fulfill it because at this Mass on Sunday, I repeat, they publicly pray for the Pope and for the bishop. They profess the same faith, and they have no intention to separate themselves from the Catholic Church or to deny the authority of the Holy See. Therefore, I consider participation in these cases valid also for fulfilling the obligation of Holy Mass on Sundays.