CathInfo.com

Cardinal Newman in his Letter to the Duke of Norfolk (certainly the least valuable of his published works), supports the bizarre thesis that the final determination of what is really condemned in an authentic ecclesiastical pronouncement is the work of private theologians, rather than of the particular organ of the ecclesia docens which has actually formulated the condemnation. The faithful could, according to his theory, find what a pontifical docuмent actually means, not from the content of the docuмent itself, but from the speculations of the theologians.

As has been pointed out, it's hardly possible that St. Pius X himself studied the profusely voluminous writings of Newman.  What he was endorsing was some apologetical work from a bishop who cherry-picked the Catholic-sounding quotes from Newman.  Newman, like all Modernists, as St. Pius X himself stated, blended orthodox Catholic propositions with Modernist ones, so someone who wanted to be an apologist for Newman could merely cherry-pick the Catholic-sounding ones to put together an apologetic piece.

Cardinal Manning stated that Newman was guilty of at least 10 heresies, and several bishops in the UK denounced Newman to Rome for heresy.  Newman was allied with the excommunicated Dollinger in agitating against papal infallibility and then reluctantly paid lip service to it on a prorivional basis, with the hope that a future pope would come along and correct/revise it ... textbook Modernism.  In fact, some of the dissidents thanked Newman for his development of doctrine position because it enabled them to retain office by paying lip service to infallibility with the understanding that it was still "under development".

St. Pius X, while a great saint, was only human, and he made a mistake in endorsing Newman based upon his misplaced trust in the bishop who wrote the book that he was endorsing.  Archbishop Lefebvre, while a saintly man himself, made some poor judgments in putting his trust in the likes of Fr. Schmidberger and Bishop Fellay (among many others) ... or allowing Urrutigoity to enter STAS, etc.  Archbishop Lefebvre made quite a few mistakes, but he's only human.  And Archbishop Lefebvre will undoubtedly be canonized some day despite these mistakes.