It will not do, therefore, to point out that on occasion Francis acts like a Catholic, such as when he “excommunicates” some uber-liberal, or when he says we must preach the Gospel, or when he insists on being faithful to the Church or condemns abortion. This is simply an old trick of the Modernists, one St. Pius X exposed long ago

Even when he does the bolded, he isn't talking about the Holy Catholic Church.  He is speaking of "the Church" as described in Vatican II.  

http://www.papalencyclicals.net/Pius09/p9nostis.htm

16. All who defend the faith should aim to implant deeply in your faithful people the virtues of piety, veneration, and respect for this supreme See of Peter. Let the faithful recall the fact that Peter, Prince of Apostles is alive here and rules in his successors,[10] and that his office does not fail even in an unworthy heir.[11] Let them recall that Christ the Lord placed the impregnable foundation of his Church on this See of Peter[12] and gave to Peter himself the keys of the kingdom of Heaven.[13] Christ then prayed that his faith would not fail, and commanded Peter to strengthen his brothers in the faith.[14]Consequently the successor of Peter, the Roman Pontiff, holds a primacy over the whole world and is the true Vicar of Christ, head of the whole Church and father and teacher of all Christians.[15]

17. Indeed one simple way to keep men professing Catholic truth is to maintain their communion with and obedience to the Roman Pontiff. For it is impossible for a man ever to reject any portion of the Catholic faith without abandoning the authority of the Roman Church. In this authority, the unalterable teaching office of this faith lives on. It was set up by the divine Redeemer and, consequently, the tradition from the Apostles has always been preserved. So it has been a common characteristic both of the ancient heretics and of the more recent Protestants -- whose disunity in all their other tenets is so great -- to attack the authority of the Apostolic See. But never at any time were they able by any artifice or exertion to make this See tolerate even a single one of their errors.