I think this song is predominantly talking about the US Government particularly during the Kennedy assassination (the line about Zapruder being the most obvious connection) Abraham Zapruder was the man who caught on film the shooting of JFK on Dealey Plaza in Dallas, Texas.
The title itself I believe refers to the CIA cover up of the assassination, evidence has refuted the lone gunman (Oswald) theory and it's practically a known fact that the Mafia was involved in the hit. The CIA had consorted with the Mafia in their numerous attempts to kill Castro and its thought the men who killed the President were in collaboration with the CIA if not acting on their authority. Some elite members of the Government even had these suspicions but it was widely thought amopngst them that the truth would cause chaos in America a nation that was mourning its beloved President. If the public found out that foul play within the administration was accountable the consensus among the government was that America would collapse into turmoil with its International image of the 'Democratic land of the free' torn to shreds and its citizens turning against its own leadership (especially Lyndon Johnson who was to replace Kennedy and known to have his issues with the fallen President and his brother.)
hence

if white america told the truth (referring to its men in Government and the CIA regarding the Kennedy assassination) its world would fall apart.

Other supports to this thinking is the opening lines

Images of perfection, suntan and napalm

'Images of perfection' could refer to the President and the first lady who were always described as a youthful, glamourous, Hollywood couple, the epitome of a perfect husband wife partnership.

Grenada - Haiti - Poland - Nicaragua

Kennedy visited the first 3 countries and his administration and governments before and after his were embroiled in Nicaragua

Who shall we choose for our morality

Possibly referring to Kennedy being the symbol of martyrdom for Americans, a man who died for the country and what he believed in, going against the will of the CIA and Pentagon and trying to broker peace with the Soviets and avert Nuclear war, a man who was the first president who tried to ratify Civil Rights legislation and who was an advocate of Civil Rights and integration (another policy where he made enemies.)

I'm thinking right now of Hollywood tragedy

Hollywood tragedy being the destruction of the glamorous and good looking movie star like JFK and the Kennedy 'New Frontier' administration.

Cuba, Mexico can't cauterize our discipline

Cuba was a burning issue at the forefront of Kennedy's entire Presidency and he never let the unscrupulous Joint Chiefs of Staff and the CIA bully him into a US invasion of the 'Soviet outpost'
hence the 'can't cauterize our discipline' meaning we the Kennedy's have morals and scruples and won't be forced to act on Cuba.
the mention of Mexico may be because of the fear that Castro wanted to insight other Communist insurrections in South America, (also as a side note its said that Oswald traveled to Mexico to try and get a visa to enter Cuba.)

Your idols speak so much of the abyss

Kennedy loyalists who were distraught after the murder (including RFK) who feared the truth who plunge the nation into chaos. RFK himself at first even though he knew it to not be true, endorsed the Warren Reports 'lone gunman theory' at the urging of some govt officials like J. Edgar Hoover (who was anti Kennedy and was undoubtedly involved in the cover up) whom said any mumblings of a conspiracy now would create a public furore.


Yet your morals only run as deep as the surface

May refer to the rumours of Kennedys contradicting policies on Cuba, although he was totally against any military action in Cuba (which disgruntled anti Castro Cuban Exiles adding them to the list of possible suspects into the Kennedy death) there was some evidence that suggested Kennedy did want to overthrow the Castro regime. Some people also come up with the ridiculous notion that Kennedy was only active in the Civil Rights crisis to secure the black vote and his political future.

and thus the possible origin of the 'morals running deep as the surface' line

Zapruder the first to masturbate

Already commented on above. Zapruder was the man who caught the assassination footage on his own camera

The world's first taste of crucified grace

Kennedy being the crucified grace a slight comparison to Jesus may be in that he was slain for doing his duty for his country and citizens in keeping them out of Nuclear destruction and wanting to achieve detente with the Soviets and equal rights for African Americans.
Jesus died for ours sins.....

its a rough interpretation I'm typing quickly without much articulation but I think there's at least some truth in it

also just to add

Fuck the Brady bill
Fuck the Brady bill


refers to the Ronald Reagan assassination attempt

the bill (which became the hand gum violence prevention act, saw to it that Americans needed a background check to purchase firearms) was named after a man who was shot during the assassination attempt.