When the title of post itself not only asks questions about trust including 'Are you trustworthy?' How can anyone be faulted for responding on a very personal level--it is a personal question unless you do a lot of clarifying in the body of the OP!
To me there's a difference between
trusting someone (where/however you meet them) and between accepting what they say about themselves as true on a contingency basis until/unless they say/do something to reveal they exaggerated, omitted info or outright lied. If they are not seeking $$ or

from me i see no risk in accepting what they say about themselves at 'face value', reserving the right to change my mind if contradictory evidence comes to light. Choosing to to trust someone does indeed, as someone pointed out earlier, have a component of needing to consider if and how they might negatively impact your life. This is one reason why once trust is broken with anyone it is very hard to restore.
Online most people have very little real power to hurt you in any substantial way unless you give it to them. i have cyber friends i've known for close to 15 years--in that time they have been consistent in what they reveal about themselves in terms of personal history and facts and in how they behave towards others. i trust some of them more than i trust some people i've known out here in 3D world.
As for my own trustworthiness i can only say that i put a good bit of energy into saying what i mean, and meaning what i say. There are people who might consider me duplicitous because they mistook my tendencies toward kindness and compassion for weakness and so they are angered when i won't tolerate certain behaviors toward either myself
or others. Because here/now incarnate i am human and subject to human emotions, while i've exerted some control over some tendencies like all of us i'm a work in progress. i tend to think of myself as a pragmatic optimist or optimistic realist. Meaning i
KNOW the difference between how the world is, people are and how both could be if more people valued concepts like honesty and compassion more than they value things.