The question is in the subject. There are post-Vatican II canonised saints that I never refer to as saints. For example, I never refer to Pope John Paul II as Saint John Paul; II. For me, a saint is one who has been a 100% traditional Catholic in everything. Are there any rules that make it compulsory in any way to address someone like Cardinal Newman as a Catholic saint?

I don't believe that the V2 church or V2 'Popes' have any authority, lest the Church defect and teach error, and lead souls to hell. I don't see how JP2 could be a Saint when he prayed with false religions...

Generally, yes, it would be wrong for a Catholic not to call a saint a saint.  In fact, the solemn canonization formula orders that the entire Church render due veneration to the canonized saint.  And it's actually a very strong argument against the legitimacy of the V2 papal claimants that they've made bogus canonizations.

JP2 is a saint of the Conciliar Church, not the Catholic Church. The two sometimes share persons, or even real estate. But the two are wholly distinct from one another. Like oil in water in a vessel, they can be forced together in the same location, but they never truly mix.

And St. Pius X was the first Pope canonized in the nearly 400 years since St. Pius V.  But now we have this astonishing run of saint-popes not seen since the days of the Pope martyrs in the early Church, Saint Roncalli, Saint Montini, Saint Wojtyla.  They're working on beatifying Luciani (JP I) also for his 33 days in office.  With such a line of saintly popes, we should be experiencing the greatest renewal of the Church since the Counter-Reformation.  But, alas, somehow we've witnessed the greatest destruction and decay in Church history.  Imagine how bad it would have been had we not had these saint popes.  It reminds of when people died of the jab and people would say that at least they were saved from COVID by the jab.

These are obviously political canonizations, basically an attempt to canonize Vatican II itself.  Most V2-era canonizations have been political in nature, and we have a plethora of affirmative-action "saints" now in the V2 pantheon.

But you hear St Thomas Aquinas referred to as "Aquinas" all the time, ditto for Peter, Paul, and so on.  Prescinding from whether a canonization is valid or not (due to a school of thought that says post-Vatican II canonizations are bogus), so far as I am aware, there is no strict requirement to refer to saints by the title "Saint".  Even in the Roman Canon, the various saints and martyrs are named without interposing "Saint" before each name, and the appellation "St Mary" isn't normally used except for names of churches, hospitals, schools, and so on.

I don't believe that's what OP meant.  I think that the question was more whether we're required to regard them as saints.  It's done often out of shorthand to simply refer to Aquinas, Bellarmine, Augustine, et al.