They have their reasons. In fact it's usually spelled out plain and clear in the dialogue, in my opinion.
Saru is upset with Burnham for what she did on the Shenzou. But he's also afraid of what she's capable of and wishes she wasn't on the Discovery. He didn't appreciate the way she used him as a threat detector for Ripper, even though when you think about it, not informing him makes the experiment 'purer', so she was being logical then. Saru has been on the ship for less than six months. He is a naturally aloof sort of alien. Notice he drinks tea alone. He does have some reservations about Captain Lorca's methods and I presume he hopes his more cautious approach will help to temper Lorca's fearless and aggressive tendencies when it comes to ship's protocols and command decisions. He also appears to be the sort to try to be polite and non-confrontational. That doesn't mean that he can't be passive aggressive when he wants to be. But he also seems to give credit where it's due and can be magnanimous at times. Plus we found out that he felt devalued by Burnham, that she didn't always treat him well before. This is supported by the novel set just prior to the events of the premiere.
Stamets articulated his reasons for being cranky and aloof to Burnham, having a mutineer dropped in his lap to babysit. But also has plainly stated several times why he's not happy with his role on the Discovery. He's been drafted into the war and had his research objectives changed against his will. This is a big issue and continues to be one. He's foremost a peaceful scientist who wants to innovate, push technologies further for the benefit of the Federation. He doesn't want to be the next Oppenheimer developing a weapon to be used to kill other species and therefore resents Lorca for constantly riding him. And yet we still get glimpses of his less pissed off side. His desire to communicate with his mushrooms. His softening towards Burnham when her scientific curiosity started shining through. His attempt to quip to Culber and play down his injuries. This guy has a dry sense of humor. I'd love to see that come out more.
Lorca is an 'ends justifies the means' type captain who values results over building ship rapport. He does appreciate loyalty, but it appears to be somewhat transactional or power based, rather than mutual. He can be charming, but it comes across as also calculated and a touch insincere. He has interests in how wat is waged and how to use the tools of war efficiently. Does that make him a war monger, though, as Stamets called him? Time will tell, in terms of how ruthless or driven to succeed at all costs he is. But Landry did offer her opinion about this and it was also a warning. And yet she seemed enamored of him, or at least driven to please him and pressured to perform. I don't know if this man is capable of making friends with his crew, that would mean seeing them as equals not assets at is disposal. He seems content to be the boss, the herder of cats, the bully, the cajoler - whatever gets results. In that regard I think he's a bit unpredictable and pretty fascinating. That doesn't make him a 'good guy' though, and certainly not the moral center of the show.
Tilly didn't want to be seen with Burnham initially because she's hyper-aware of her status and wants to advance in her career and keep up appearances that she's a model officer. She handled herself well on the away mission. She was calm and collected and did her job with aplomb. Yet she is socially awkward and runs her mouth off at times. That said, she's been reaching out to Burnham and trying to make friends with her. While Burnham has remained aloof at times, we still see in the latest episode a warming to her room-mate. Even the "Tilly..." sounded softer and more affectionate. Tilly deliberately bent the rules to help Michael with Ripper, and in return she gave the Cadet gratitude. There's definitely some bonding going on, even if it's tentative for now.
Perhaps the show would benefit from more around the conference table banter, but it seems to me that Lorca only consults when he wants to and prefers to keep the command decisions top heavy. Let's hope that in coming episodes we'll get different mixes of the crew and more glimpses as to other aspects of their back history and personality.
