There are, I think, two sets of issues here.

One is how offensive the videos were, or were not--especially in the ship-board context in which they were shown. I also think it is rather hard to make a complete judgment based on the selected excerpts that have appeared online.

Second, there is the judgment that Captain Honors demonstrated in showing the videos, repeatedly, to 5,800 diverse members of the Enterprise crew. I would venture that around 75% of the American public would have predicted that these videos a) would eventually leak, and b) when they did, they would likely adversely impact the image of the US, the USN, and the career of Captain Honors. I further imagine that 95% of all federal employees (including clerk-typists, drivers, and janitors) would have predicted the same.

The question then becomes whether you really want command of a CVN in the hands of an officer whose sense of the cultural, media, and political context (outside the bulkheads of his aircraft carrier) really falls in the bottom 5-20% --especially if, in a crisis, he might be called upon to use that range of skills. Can you really trust that an officer who misleads a visiting Hollywood star into appearing in a sophomoric video won't do the same to a local dignitary during a diplomatic port call?

Provided Captain Honors understands how his well-intentioned actions could be problematic (and learns from that), I see no reason why the incident should be a permanent handicap to his future navy career. However, the notion that senior command officers can blithely act as if they weren't embedded in a broader world is hardly anything that any military should want to encourage.