Trust is such a poor and overloaded word. What is Mozilla "trusted" to do? That's a very difficult question to answer.
Perhaps thinking in terms of expectations would be better: My expectation is that Mozilla will produce a decent browser, with occasional bumps and steps backwards in response to some flavour du jour, most notably in the area of wouldn't it be cools that break usability. Not to mention the mobile browser considering my tablet and phone to be the "same type of device", when my tablet is much closer to my computer - and it's the computer's UX I want everywhere, not the phone's.
My expectation is that Mozilla will produce a half-decent email client that I have no real reason to use.
My expectation is that in doing these things Mozilla software will mostly stay out of my way, mostly work as I expect (sync the function works pretty much as expected, sync the UX is awful - I still need all manner of extension and app to get the "move easily from one device to another" experience I really want).
My expectation is that Mozilla will occasionally cook up something new, e.g., Persona, that I really don't see a need for, and that Mozilla will be unable to articulate why that new thing is needed, cool, or anything else.
If Mozilla disappeared tomorrow, I would be quite upset, because FF sucks far less than every other browser - maybe that's because I am so used to it, that I've made it work for me, but moving to anything else would be painful. My expectation is that they will continue to deliver excellent B+ software that is adequate to my needs and wants.
But why on earth would I expect that I could trust Mozilla with anything more than my sync information?
I trust Mozilla about as much as I trust my bank, as much as I trust Google, and, to be fair, more than I trust facebook. But again, trust is the wrong word: I expect Google to mine my information, make the occasional misstep, but to by and large attempt to keep my information safe and secure, because if they don't, it ain't just mine they release, it's millions of ours, and they cannot afford that.
I expect my bank to mess up UX occasionally, but to do security reasonably well, and to not share my personal overmuch, because of the regulatory framework in Canada: They just cannot mess this up without serious consequence.
I expect facebook to mine, share, intrude, mess around, and generally do stupid things. I am never disappointed.
What should I expect of Mozilla Accounts?
Nothing. Nothing at all, because "Accounts" is so not what I think of when I think "Mozilla". I hear "Mozilla" I think "FireFox", I think half-decent browser, better than others, adequate email client, neither better nor worse, I think confusing cross-device UX...
...but do I think trust?
Nope.
And the "occasional bump in response to something shiny" mentioned above means I never will - at least not without major public rebranding.
If I am going to trust you, you need to convince me you are rock-steady reliable, and never prone to blowing with the wind.