It is indeed very sad to read that sermon. How far the Society has fallen.
Fr. Laisney's equates refusing communion with people who do not confess the Catholic Faith but publicly confess heresy to refusing communion with wicked men (sinners), of which the former is Catholic doctrine, and the latter Donatist heresy. You can find this is the last paragraph on page 1, as well as the last paragraph on page 3 and the first on page 4.
By making this his main argument Fr. Laisney is creating an ecclesiology according to which Catholics and modernists (and modernism is a heresy) are both a part of the Church, a strange church where Catholics must remain in communion with heretics in order to remain Catholic and to remain in the Church. He even recognizes that Francis is a modernist two times, which is so obvious that he couldn't deny it even if he wanted to (you can find all of this in paragraphs 4 and 6 on page 2, and in paragraph 4 on page 4).
That, of course, is totally opposite of the what the Catholic Church teaches and what it is. There are no public heretics in the Catholic Church, only Catholics. Those who commit public heresy are not in the Church and no Catholic is obliged to be in communion with them. In fact, the Apostle explicitly tells us to avoid such men. We are obliged to avoid heretics.
But what Fr. Laisney is actually saying is that public heresy is merely an evil act, a sin, and not enough to separate someone from the Catholic Church. That is an error, and this error enables him to create a Church which contains both Catholics and public heretics, a Church which is therefore not united in Faith, which means that it is neither One, nor Holy, nor Catholic. The Church which he thus created in his mind is actually the Conciliar Church, which he calls "the visible Church", and which contains both Catholics and heretics (you can see this quite clearly in the first paragraph on page 3).
He then invokes Abp. Lefebvre, who would be the first to condemn this equating of the Conciliar Church with the "visible (Catholic) Church", as he already did in 1989:
This talk about the "visible Church" on the part of Dom Gerard and Mr. Madiran is childish. It is incredible that anyone can talk of the "visible Church", meaning the Conciliar Church as opposed to the Catholic Church which we are trying to represent and continue. I am not saying that we are the Catholic Church. I have never said so. No one can reproach me with ever having wished to set myself up as pope. But, we truly represent the Catholic Church such as it was before, because we are continuing what it always did. It is we who have the notes of the visible Church: One, Holy, Catholic, and Apostolic. That is what makes the visible Church.
Fr. Laisney leads himself into such an irony in the second paragraph of page 4 - he affirms that "there are sins of the priests which forbid the faithful to participate with them: and such are the sins against the unity of the Church".
Now, public heresy is also a sin against the unity of the Church. Therefore, what he is actually affirming (without knowing it, obviously) is that Francis' sins of public heresy forbid the faithful from "participating with him".