From Wikkipedia
According to Wikipedia, quoted below, each sport was allowed to make its own rule after 1970. So the FEI must have changed the rule for equestrian sports?
"Initially, only amateurs were considered such; professional athletes were not allowed to compete in the Olympic Games. A short-lived exception was made for professional fencing instructors. This exclusion of professionals has caused several controversies throughout the history of the modern Olympics. 1912 Olympic pentathlon and decathlon champion, Jim Thorpe, was disqualified when it was discovered that he played semi-professional baseball prior to winning his medals. He was restored as champion on compassionate grounds by the IOC in 1983. Swiss and Austrian skiers boycotted the 1936 Winter Olympics in support of their skiing teachers, who were not allowed to compete because they earned money with their sport and were considered professionals.
It gradually became clear to many that the amateurism rules had become outdated, not least because the self-financed amateurs of Western countries often were no match for the state-sponsored “full-time amateurs” of Eastern bloc countries. Nevertheless, the IOC, led by President Avery Brundage, held to the traditional rules regarding amateurism. In the 1970s, after Brundage left, amateurism requirements were dropped from the Olympic Charter, leaving decisions on professional participation to the international federation for each sport. This switch was perhaps best exemplified by the American Dream Team, composed of well-paid NBA stars, which won the Olympic gold medal in basketball in 1992. As of 2004, the only sports in which no professionals compete is boxing and baseball (though even this requires a definition of amateurism based on fight rules rather than on payment, as some boxers receive cash prizes from their National Olympic Committees); in men’s football (soccer), the number of players over 23 years of age is limited to three per team."