You can still travel to Cuba legally with a US passport. You simply cannot travel to Cuba under the “People to People” category (which was primarily used by guided tour companies and cruise lines). You can still travel to Cuba, 100% legally, under the “Support for the Cuban People” category.
What this changes about Cuba travel:
Existing plans will not be affected. If you planned your trip under the People to People travel category before June 5, your trip will be grandfathered in (i.e. your trip is exempted from the new regulations). If you planned your trip under the Support for the Cuban People category, your trip will not be affected in any way. Airlines are still flying to Cuba, and it is still 100% legal to travel there.
The only exception: American cruise ships are no longer able to go to Cuba as of June 5, 2019. If you booked a cruise to Cuba for June 5th or later, contact your cruise company.
What this means for the future of Cuba travel:
You can no longer book trips to Cuba under the People to People travel category. This will affect your ability to take guided tour packages and cruises to Cuba, as American cruise ships are no longer able to dock in Cuba. However, you can still travel under the Support for the Cuban People category.