The answer is that St. Athanasius is the one who informed them, which is why they were enlightened about it, and had the authoritative backing to confidently do what they did.
Unfortunately, that is your view. But it is mistaken. Truth is simple, yes, and sometimes it is not that simple. But for Bp. Williamson to reject something just because it is "black and white" is a false Liberal belief.
The fact is - no true pope could be the head of the true Church, simultaneously with being the "head" of a false, heretical Church. That is a diametrically opposed proposition to Catholic teaching....meaning it is absurd, doctrinally, and an error against the Faith.
Some opinions are true, and some are not. We have to face that fact. The word "opinion" is not a license to reject a proposition out of hand.
From what I recall, St. Athanasius did inform them, though he was not the only one to speak out against the error of Arianism, of course.
However, you said in reply #19 today: "...and the true Catholics at that time wasted no time in refusing communion based on their own judgment..[...] The True Catholics at that time refused to go to their Masses, even though they were valid Masses and had valid sacraments."
Perhaps you did not intend to make it seem as if the Catholics at that time refused communion based only on their own judgment, but that's what I took it to mean.
You mentioned above that..."But for Bishop Williamson to reject something just because it is "black and white" is a false liberal belief." I never said that Bishop Williamson rejects SVism because of the "black and white" issue. That's not the same thing at all as what I said. I said that Bishop Williamson says that SV's need to see everything in black-and-white.
So, the Catholic lay faithful did not make the judgment all on their own regarding the errors of Arianism, but rather they trusted in the leadership and judgment of a bishop, St. Athanaius. Just as many of us trust in the judgment of Archbishop Lefebvre. Not that he was perfect and got everything correct.
I've seen the study of Bishop Tissier de Mallerais regarding the belief that the Pope is the head of two churches. It makes sense to me, though it is difficult to read.
I agree that some opinions are true and some are not. And I agree too that this in itself isn't a license to reject a proposition out of hand.
And lastly, you said that "no true pope could be the head of the true Church, simultaneously while being the head of a false, heretical church." This statement of yours is not one with which the R&R would agree, I don't think. The conciliar church still has some aspects of the faith left. It isn't completely heretical. It's view of the SV's that the conciliar church is completely false. Please don't infer that non-SV's take this view (though perhaps some non-sedes do)
Bishop Tissier de Mallerais explains it quite well in his study, which can be found on Dominicans of Avrille website. He wrote that the conciliar church is like a parasite that feeds off its host (the True Church), and that there is a transfer of substance, so to speak, from host to parasite. He says more of course, but that's what it basically boils down to.