There seems to be a common belief that trustworthiness, or lack thereof, is the sole criterion controlling whether a person will be granted access to military secrets. It also seems to be believed that revealing a secret is a common method of confirming trust in an individual.
As someone who in real life held a security clearance in the US military for 20 years, I can affirm that these ideas are ridiculously false.
The chief criterion that controls whether a person will have access to information is the principle of Need to Know, specifically, whether a person needs to know something in order to accomplish his or her official duties. It does not matter how trustworthy you are, how "important" you are, or how high your rank is; if you can get your official duties done without having access to information A or location B, sorry, no, you don't have access. Material at the highest classification levels will not only be marked with its classification, but will also be marked to indicate the program under which it is classified, and people who aren't briefed into that program are presumed to lack need-to-know.
The chief reason for this principle is because the chance of compromise increases as the number of people with access goes up; giving access to people who don't need it creates an unnecessary risk, and while the enemy has many ways of getting a person to reveal what they know (torture, bribery, going through their trash, etc.), nobody has found a way to get someone to reveal a secret they don't actually know.
In my own case, I was a cryptographic maintenance technician. (Cryptographic equipment is used for encrypting messages for transmission so that whoever intercepts the message traffic sees only pseudo-random garbage.) As part of my job I had access to the equipment, the maintenance manuals for the equipment on which I worked, and the operations manuals for the equipment (because you need to know how to operate equipment to know if it's operating correctly). I also had access to the facility where the equipment was used, although in some cases I still had to be escorted, because my duties did not require me to come and go according to my own judgment.
I was most certainly not allowed to peruse the message traffic of the equipment I maintained, even though I held a clearance equal to or higher than all of this message traffic. This was not a slight against my trustworthiness, nor did it cause me to wonder what my chain of command was hiding from me; I didn't need to see it to do my job, so I wasn't allowed to look. It must be understood that nobody in the military has any problem with this.
In the case of a person who has a need to know something, but who does not have the required clearance level, the military will either verify the person's reliability and grant the clearance, or arrange that person's duties so that access is no longer required.
So no, Rose does not get briefed on the plan; she simply does not need to know. Finn does not get briefed on the plan; he doesn't need to know, and has glaring reliability issues (i.e., he was one of the enemy a few days ago). Poe would have gotten briefed if Holdo needed him to know, but she apparently decided that either he wasn't going to be involved in the evacuation except as a passenger, or that informing him could wait until later, and she was acting perfectly within her authority to make these decisions.
We can question the wisdom of a plan that excluded the active participation of someone as skilled and experienced and otherwise unoccupied as Poe, and the condescension she exhibited towards Poe when handling his questions was frankly inexcusable, but once she had decided on the roles of everyone involved in the plan, determining that certain people don't need to know the plan is perfectly within her authority.
