There are three reasons we should not go into conciliar churches to pray:
Places of evil are inherently very unfitting places for prayer and for offering the True Mass. The Mass and the Blessed Sacrament are among the very best and most sacred “Things”. To mix these best with the worst (viz., an evil place) is most unfitting and offensive to God. It is like choosing the filthiest, most disgusting vessel as the container for the most precious liquid—it is wholly unfitting.
As always, the Summa explains this truth admirably:
Now although, properly speaking, a corporeal thing cannot be the subject of the stain of sin, nevertheless, on account of sin corporeal things contract a certain unfittingness for being appointed to spiritual purposes; and for this reason we find that places where crimes have been committed are reckoned unfit for the performance of sacred actions therein, unless they be cleansed beforehand.
Summa Supp. Q.74, a.1, respondeo (emphasis added).
But sins directed against God are the gravest sins—much worse, for example, than the crime of murder, because murder is a sin directed against man, not God. Summa, IIa IIae, Q.13, a.3, ad 1.
new mass is inherently protestantized and man-centered and so is
irreverent treatment of the Sacred (the definition of a
IIae, Q.99, a.1. Thus, the new mass is objectively worse than
murder, since the new mass is objectively a grave offense directed
against God Himself.
If a new mass is valid, that makes it objectively worse—by being a valid (rather than invalid) sacrilege. A valid sacrilege even more strongly calls down the wrath of God because a valid sacrilege compels God Himself (Sacramentally present) to take part in the sacrilege.
Thus, conciliar churches are inherent dens of sacrilege because the new mass is said there (and for many other reasons). As a den of sacrilege, it is a very unfitting place to pray or to offer the True Mass. Summa Supp. Q.74, a.1, respondeo.
In the proportion in which we love Our Lord, we should abhor conciliar churches. This is like a widow who loved her deceased husband. In proportion to her love for him, she would not wish to use as a place of amusement, rest, and comfort the location in which her husband had previously been tortured and brutally murdered. Her love would not permit it.
Similarly, those who love our Lord and realize that the new mass is objectively a sacrilege, would never wish to be in a place which continues to be used for the new mass. And the more an informed Catholic loves Our Lord, the more he finds conciliar churches intolerably odious—more because of the sacrileges that continue to occur there than because of the buildings’ conciliar ugliness! This is a second reason informed Catholics do not enter conciliar churches.
Scandal is giving the appearance of evil which makes another person more likely to sin. Summa, IIa IIae, Q.43, a.1, ad 2.
To the extent others see us entering a conciliar church, it gives scandal because this would tend to give credence (in their minds) to what goes on there. Most people would not make the distinction when we entered a conciliar church, e.g., to pray the rosary but not when the new mass is said there. Each person’s presence adds a little to the appearance that the conciliar church is more visited/attended and that what goes on there is more accepted.
Without thinking deeply about the matter, many people would tend to think that those entering a conciliar church approve what is happening there. Therefore, in the eyes of many people, we would indicate our approval generally, for what goes on there, regardless of our real opinion. Because people are social creatures, they would tend to accept the conciliar church because they see other people accepting it. This is a third reason that informed Catholics do not enter conciliar churches.