I think it depends a lot. I just got off of the Celebrity Edge's June 26th sailing (the first sailing from the US) and I have to say that it was easily the best cruise I have ever been on. The enthusiasm from the crew, from bow to stern, was overwhelming. There were a few things that weren't as smooth as they will be on later sailings (a few people complained that pacing in the dining rooms was a bit off), but generally speaking while we were on the ship the only really visible differences were that the crew was wearing masks, and they served us at the buffet. It just felt incredibly normal, but with 60% fewer passengers.
Having said that, our sailing was 98% vaccinated, so protocols were a bit different than they would be for Disney. While the CSO may not be regulatory after July 18th, I don't think any cruise line will voluntarily open themselves up to the liability that would come with sailing contrary to CDC guidance. (And I fully expect the CDC to release a revised set of regulations before Disney sails.) I think that the protocols for Royal Caribbean's Freedom of the Seas are illustrative of what path Disney might take ... they represent a fairly normal experience for vaccinated passengers, but tighter protocols and restrictions for those who aren't:
https://www.travelpulse.com/news/cr...als-protocols-for-unvaccinated-travelers.html
The other thing I'll mention is that protocols in different ports of call are constantly changing, so no matter what I wouldn't sail on an early sailing unless I was willing to deal with changing plans. 3 days before our sailing we were told that we would only be allowed to leave the ship in Mexico on a Celebrity-arranged tour, then the day before we docked in Costa Maya they told us that we could explore on our own there, but we'd still be restricted in Cozumel. So it's not just the days leading up to the cruise when things are changing.