When I meet a new traditional priest I say, "Fr., the New Mass is a mortal sin and there is absolutely no salvation outside the Church, what other questions do you have for me?" Outside of this, there should not be any other questions. I could see if some guy is handing out Natural Family Planning literature (birth control) at the local Trad chapel, then yes, the priest might kick him out, but for the most part all these other issues are a distraction.
Even our Trad seminaries do not always focus on the foundational literature. When I was at St. Thomas Aquinas ('94-97) we should have read The Great Sacrilege, which was the first serious critique of the New Mass. I think the attitude- if I might critique the minds in control at the time, was probably- "Fr. Wathen is a Feeneyite, so therefore we cannot read his book The Great Sacrilege."