PBA: (What process the tzedukim used is not clear to me; I am skeptical of the second grade pshat that they didn’t hold of any torah sh’baal peh.)
AFAIK this pshat is pretty clear around shas and Rashi repeats it a multiple times. Much like some ultra-Modern “Orthodox”, they knew all the halochos, learned it carefully, but rejected torah sh’baal peh.
(OK, of course ultra-MO are not in practice nearly as extreme, and don’t reject torah sh’baal peh, just some parts of it which they see as divisible from the rest and incompatible with their worldview.)
As an example, see end of Sukkah 43b where they purposely disrupted a mitzvah by making it impossible to use the avrovos without violating a issur derabonin. The meforshim gives various peshotim exactly which issur derabbonon were involved but all agree the Tezdokim (in this case Baisusim, specifically) knew the the intricacies of muksa very well (no doubt learned all day in a beis medrash) and used that to knock the chachomim and disrupt mitzvos.
YCT and the ilk appear to have similar animosity to the parts of torah sh’baal peh they don’t like. Some non-ultra-MO can stray into this territory too at times; the MBP issue is an example of not just disagreeing with mesorah/halochoh if it gives a bad impression, but actually helping disrupt it instead by giving public support to its detractors, just because it’s gives a bad impression in the 21st century.