The word ‘Jew’ is just a shortened form of the word ‘Judean.’
So when Mark and John spoke of the Judeans, they were usually referring to people that lived in the Roman Province of Judea. You see, Jesus and eleven of his Apostles (although likely all from the tribe of Judah) lived in the northern province of Galilee. The Judeans called them Galileans (Mark 14:70), while the Galileans referred to the people in and around JeruSalem as Judeans (or Jews).
With this knowledge, it’s easier to understand what the scriptures mean when they speak of the water jars at wedding reception at Cana being there for the ‘Judeans’ to wash in (presumably since they had to travel far), and that the ‘Judeans’ were looking to kill Jesus, and that the ‘Judeans’ rejected Jesus. In these cases, the texts aren’t referring to the nation as a whole, but to the people that lived in Judea and/or in JeruSalem.
It seems that Jesus was widely recognized as a Prophet and as God’s Anointed One in Galilee. However, it was in and around JeruSalem (the center of Jewish worship and various Jewish sects) that Jesus was finally rejected and turned over to the Roman governor for execution.