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Traditionalism is about MORE than the mass.  

Much more.
It's also about doctrine, belief (internal adherence and external profession), piety, spirituality, and living more than superficially the Traditional liturgical seasons.  
It's about knowing WHY we believe as we do.
It's about understanding and assenting to the fundamental superiority of the Traditional Mass, with its vertical spirituality ordered to mankind's obedient relationship to God, as His subjects.  We should know these truths well enough to be able to explain them to other Catholics and non-Catholics.
It's about a conscious hunger and dependency on all of that, which should permeate our identity.

Traditional Catholicism is not about a patchwork of beliefs and practices -- some from the N.O., some from Traditional Orders -- but a seamless identity.

Simply because of age, most trads of today were poorly catechized as children and adolescents.  Those in the best position are the ones who grew up with genuine Tradition and excellent catechesis, both, and have remained traditional.  (Lots of trad-trained elderly folks are N.O.) 

If a trad was fortunate enough to convert from outside the faith through a traditionally trained and formed priest, their catechesis is probably better than someone who went simply from the almost non-existent catechesis in the N.O. to attending the TLM, rather than actually learning about Tradition.  

Trad priests should actually insist on examining their parishioners or flocks as to their level of knowledge, and those needing catechesis should be required to attend, under his supervision and direction.  JMO.

The issue of changes to schooling is separate from the changes to the Mass.  The new mass came first, and was the priority.  All else came after the new mass was already accepted.  If you were corrupted by the new mass, your Faith was already damaged (and for many, on life support), even if your schooling was mostly "normal".

So then you admit that someone could be traditionally educated in their Catholic faith even after the promulgation of New Mass. How exactly does that help your argument at all? If anything it's the opposite, as it provides further evidence that attending the New Mass and adhering to material heresies are not inextricably linked.

Traditionalism started day 1 after Vatican 2.  Many catholics of this generation left new-rome and many priests did as well, in order to preserve Tradition.  Your description above is revisionist history.  What Tolkien did, in his particular country, is of no consequence to what 1,000s of Catholics did in America to keep the Faith.

And what exactly did those 1,000s of Catholics do? You keep falsely implying again and again that going to the new Mass means you accept abortion, gαy marriage, etc. etc. when none of those things are even teachings of the Conciliar Church, as bad as it is. A NO Catholic can likewise disagree with the Pope's ecuмenism without thinking that's a reason to not go to Mass. Whereas the largest Trad society in the world which the majority of Trad laity attends, openly teaches the most liberal form of BOD. So again, ignorance on the validity of NO does not automatically make you a material heretic, nor does being a Trad mean you're 100% orthodox. 

Traditionalism is about MORE than the mass.  Keeping the Faith is more important than the mass.  A catholic cannot attend his indult mass, where Fr X says a reverent liturgy, and ignore the fact that 2 hours later, Fr Y comes in and dances around (ON THE SAME ALTAR) and makes jokes and hands out wine and cookies.  Or worse, Fr X says both the indult AND the new mass, which is the height of hypocrisy.  This type of action is inconsistent with catholicism - you cannot accept evil to get good.  The end (having a reverent liturgy) does not justify the means (accepting the abominable new mass as the "ordinary" form).

Now for some reason you've gone off on a tangent here and you're attacking Indults rather than NOers. NOers don't realise their Mass is invalid, and they don't consider it "wine and cookies". Arguing that they're knowingly doing evil because they "know" their Mass is invalid is ridiculous, they don't know their Mass is invalid, or else they wouldn't be attending it.