Where did you get the idea that the ‘troubles’ in Northern Ireland were happening in 1966? You have your timelines screwed up here.
The thing did did not really kick off until 1969. By then the old official IRA had backed off from their ‘border campaign’ in the 1950s and had effectively demilitarised.
It was 1970 when the real violence started. By the the British troops had their role shifted away from protecting the Catholic population from Loyalist mobs with the emergence of the Provisional IRA and IRSP paramilitary groups.
By the time of Euro 1996, the Provos second cease fire was holding.
Why would the World Cup be withheld from England for dispute that was yet to start for three years? Why would the Euros be withheld after the positive move to settle a 25-year old violent dispute?