I think not because the Society of St. Pius X is not in schism. Recently, the Prefect of the Congregation for the Doctrine of the Faith, Cardinal Luis Ladaria Ferrer, openly said that the Society of St. Pius X is not separated from the Church.
There are previous documents (e.g. Eclessia Dei ) which Cardinal Castrillon and the others said that the Society of Saint Pius X is not in schism because the Pope granted them faculties for confession. It is highly unorthodox for a Pope to give faculties to hear confession to schismatic priests.
Pope Francis granted all priests of the Society of Saint Pius X faculties to hear confession. It is also a demonstration that the Pope and with extension, the Holy See do not consider the Society of Saint Pius X schismatics.
There might be canonical irregularities from a political point of view but not from the faith because when we speak of schism it encompasses everything including matters of faith. Therefore, I see no problem if you want to send your children to an SSPX school. If it is a good school that provides a good education, why not?
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