Part of the problem of having any faith in your immediate manager is your perception of whether he/she actually has the authority to sanction something if appropriate.
When the current crop of crew managers have dispensed their quota of performance managing to a less than impressed "team", there is precious little time left for dealing with the nitty gritty issues of being a lowly crew member.
How many times do you hear a genuine story of a crew member pondering whether to go to their crew manager to sort out an issue that requires a day off or change to a roster only to be advised by colleagues that it is not worth the effort, just go sick!
If you can convince your manager that you need something, anything, then he must have the ability to pick up the phone to the relevant dept and make it happen, no question, no matter what. Managers have to be able to manage effectively and to do that they need the tools to do the job.
When crew managers in BA can make informed executive decisions and action them, crew will use and trust them.