a government agency. It remit and its activity is regulated by government. And therein lies the problem. While there may be many competent and ethically upstanding people inside the service, the people setting the parameters for its activity are anything but. What GCHQ provides is used by both the Home and Foreign Office (at least) and is, therefore within the remit of the secretaries of state. Now consider that in recent time that list of political no marks in those posts has included Amber Rudd, Theresa May, Boris Johnson and Jeremy Hunt*, you begin to see the problem. In theory there is parliamentary oversight, but in reality things are much murkier (and sometimes for sensible reasons).
I am always wary of organisation with large amounts of power that are subject to direct political control, so my trust is in very very short supply, I'm afraid.
* and yes, I remember the bad old days of Jack Straw too, so it's not entirely party political.