Boule << It matters to Gerry Matatics and Robert Sungenis. It mattered enough for Gerry to get the boot from Catholic Answers years ago. >>
Now hold on, Matatics wasn’t booted from Catholic Answers over the “material sufficiency” vs. partim-partim position. At that point (circa 1990)
both CA and Matatics agreed on partim-partim (e.g. see Keating’s 1988 book which clearly articulates the partim-partim view). It was when Akin joined CA that the “material sufficiency” view came into prominence among Catholic apologists like myself

, with the first reference to it in This Rock being his 1993 side-bar article (see the quote there from Yves Congar’s book Tradition and Traditions) within the infamous Patrick Madrid “The White Man’s Burden” hatchet job of the 1993 White-Madrid debate on sola scriptura.
You see, I know my This Rock. So in other words, I agree “tradition” can be slippery, we need to be more precise.
That said, I would argue there are at least 5 specific Catholic doctrines received by “oral apostolic tradition” that don’t have clear and explicit reference in Scripture:
(1) infant or paedobaptism
(2) Mary as the “New Eve” (which developed into other Marian beliefs)
(3) prayers for the dead (e.g. although mentioned in 2 Macc 12)
(4) the primacy and authority of Rome (and hence, its Bishop) as the center of Christian orthodoxy
(5) apostolic succession, the Bishops inherit the authority of the apostles (but not their Spirit inspiration), with the Bishop of Rome especially called “the Apostolic See” as Peter’s seat of authority
Those are some specifics since evangelical apologists like to ask for them. These beliefs show up universally in the early-mid 2nd century Church (ubique, semper, ab omnibus = that which is believed everywhere, always, and by all).
These aren’t necessarily “essential” to “mere Christianity” but they are essential to Catholic theology and explain why we believe our later developed beliefs are apostolic.
Phil P