JSFiddle - React, Tailwind, and code Playground

JavaScript

var events = [
  {
    id: 'event1',
    start: new Date('1/1/1 5:00'),
    end: new Date('1/1/1 6:00'),
    hasConflict: false
  },
  {
    id: 'event2',
    start: new Date('1/1/1 5:30'),
    end: new Date('1/1/1 6:30'),
    hasConflict: false
  },
  {
    id: 'event3',
    start: new Date('1/1/1 7:30'),
    end: new Date('1/1/1 8:30'),
    hasConflict: false
  }
]

function checkFirst (event1, event2) {
  event1.start < event2.start 
    ? checkConflict(event1, event2) 
    : checkConflict(event2, event1)

  function checkConflict (first, second) {      
    if (first.end > second.start) {
      first.hasConflict = second.hasConflict = true
    }
  }
}

events.forEach(event1 => {
  events.forEach(event2 => {
    event1.id !== event2.id && checkFirst(event1, event2)
  })
})

console.table(events)