There are acceptable conditions for issuing a warrant for arrest or search, two main requirements would be: Probable cause; found when police officers have indications based on real facts or circumstances or from reliable sources, that a crime was committed or is about to be; and an Officer's Oath, this can be written or oral, this is when officers swear that no false statements have been submitted in order to get a warrant for a search or arrest from a Magistrate.
Reason they would support the Vietnam war is to support President Truman use of containment. Which was to limit the spread of communism throughout the world.
A reason not to go to war is the fear of being drafted which was common during the Vietnam War.