Your naivety is astounding. Either that or you do not pay attention to reality. You cannot convince these people we are fighting with facts, for that is exactly what they want you to do, so they can just ignore them or discount them. They are not interested in facts, and that is the fact you seem to just ignore. Wake up.
Rather, my means is not naivety, for instead it is such recourse as defending specious sources with its false headlines that plays into the oppositions hands, while using such as sources normally sanctioned by the opposition can at least put them to silence, which I have often done by the grace of God - even if not convincing them which is not an absolute necessity versus exposing their falsehoods.
. When making an argument, we need to examine if and how it could be countered, and deal with objections with valid substantiation if indeed our argument is sound. Faced with recalcitrant opposition, the Lord Jesus Himself invoked Scripture, the authority of which was accepted by the opposition, and thereby put them to silence, and exposed them as erroneous.
However, there does come a point in which such repeatedly dismiss soundly reasoned and substantiated arguments, and thus they can be left to their chosen delusions.
Grace and peace thru Jesus the Lord.