Decisions will have to be made quickly. The CONCACAF Gold Cup, the men’s soccer championship for North American, Central American and Caribbean nations, begins June 14 and will be played at sites across the United States (and one in Canada). Haiti has qualified for the competition and is scheduled to play games in San Diego, Houston and Arlington, Texas. The Club World Cup, the world championship for men’s club soccer teams, also begins June 14 in several U.S. cities. No team based in a country on the banned list has qualified, but the teams involved include players and staff members from all over the world. CONCACAF, which runs the Gold Cup, and FIFA, which runs the Club World Cup, did not immediately respond to requests for comment. Other events coming to the United States this year — including the under-19 softball World Cup and the world skateboarding championships — are less likely to be considered “major” events. There are also big races, like the Chicago and New York marathons in the fall. Mr. Rubio may find himself facing a lot of judgment calls. The implications for college athletics, where rosters in many sports are dotted with international students, are also unclear.