How did they plan to get rid of opposition to Judaism?
They planned to get rid of opposition to Judaism by killing the opponents. In Saul's case, the Grecians sought to kill him because he disputed against them and spoke boldly in the name of Jesus. The context notes that murderous attitudes are quickly aroused in religion, and killing was their method.
Les explains that after Saul came to Jerusalem, he spoke boldly in the name of the Lord Jesus and disputed against the Grecians. These were not Gentiles but non-Palestine Jews, citizens of other nations. They could not stand anyone doing anything against Judaism. So they went about to kill him. Les says nothing preempts murderous attitudes faster than religion, even Judaism. If they had opposition to it, the best way to get rid of the opposition was to kill them, and that is what they attempted to do with Saul.
And he spake boldly in the name of the Lord Jesus, and disputed against the Grecians: but they went about to slay him.