It appears from what Captain Lee has said that he was initially asked/told to be on the show by his boat owner who had chartered the boat to the production people for the show. So, basically - "this is what the boat is doing this year, so be on tv or I'll get somebody else to run it." He agreed to do it, and turns out he enjoys it and is good at it.
Presumably as part of this deal he relinquished a great deal of hiring/firing power in favor of the casting choices of the show runners.
In the normal course of running a boat, he would have seasoned professionals who required very little supervision other than from their department heads, and even the greenest of new hires would have the same strong incentive to behave professionally as most of us do in our work lives.
In the context of the show, the lower level employees are largely hired for mental/emotional instability and pre-hire expressed willingness to engage with their coworkers in entertaining ways.
I think part of the Lee/Kate dynamic is that he sees her as part of the professional old school team. Comments he made about Simone on twitter were basically "this is the big leagues - you can't open a bottle of wine, it's not our job to TRAIN you on our time/dime." He was holding her to standards of real-world hires -- but she wasn't hired for the same criteria as non-show 3rd stews would be. I'm sure he's used to a fair share of deckhand drama, but from people who overall respect the hierarchy (or who can be fired/replaced at will with someone who is). But the "cast" of this show are precisely that. They're employees of the show, and seek to please their real bosses first, the tv crew.
I think Lee respects Kate because she's still delivering the above-deck service in the manner to which he's accustomed and generally at least one of her stews is also delivering at an expected level, so he doesn't care how messy she gets in talking heads or with other employees who AREN'T delivering at the same level. He loves Courtney for many of the same reasons, I think -- hard worker, doesn't let up in the front of the guests, lets down her hair below deck, no problem with that in his eyes.
I'm not the biggest Kate fan in the world, but I think to a certain extent her behavior towards the obvious production stunt hires/less capable stews is to isolate them where they can do the least damage to the above deck service, while simultaneously providing fodder for the show. So she's serving two masters which has to be exhausting, especially when she feels ganged up on with no support from either side. (Which is not to say she's not unfairly harsh sometimes, too).
Unlike everybody else, Lee really does have the real world responsibility of moving the boat and passengers around, and the luxury of considering the tv show a side gig. Since this season being out of the tv show loop is reflecting poorly on him, I bet he is reexamining future vigilance on crew behavior, especially sexual harassment policies stated up front, and explicit "this is what 'embarrassing the boat' means" policies.
I think the Ashton/Rhylee drama and much of Ashton's behavior is influenced (not caused by) production prodding. If you watch his talking heads... he's gleefully recounting his worst behavior in a manner that suggests that it's being received positively by the person he's talking to and therefore he believes he's coming off great, even charming! Which makes me long to see the questions posed that prompt his sexual bragging. I suspect that having gotten some really rotten behavior on tape (unprovoked), they decided to home in on every worst instinct and amplify it. There was no love for him in the camera angles of the photo shoot interspersed with his "I'm so amazingly hot being with these models" giggling confessions. He thought SOMEBODY was lapping it up (because they must have been).
I don't let Rhylee off the hook of course - she truly is her own worst enemy. I hope she gets some clarity that the show is invested in her worst behavior/outcome, and it might be in her better interest to move on and try to grow out of the limelight.