To trust and to find trustworthy are very closely linked. One leads to the other naturally. You might trust someone, not because they are trustworthy, but because you need to trust someone. Then, because you trust them, you come to believe that they are trustworthy. This may not reflect the reality of that person. That sense of trustworthiness may linger, even after you stop trusting them -- and maybe that lingering sense of trustworthiness is you trusting them to some degree, despite yourself.
Are people trustworthy just because they have good intentions? Not necessarily. If we establish between two people that one of them has good intentions, that in itself may produce trust that exceeds what that person warrants. This tends to lead to betrayal.
People are more essentially their intentions, rather than their effects. God sees the person / the intentions, but we see the effects.
If we assess people on intentions, then we talk about what we don't know directly. We have to guess. But if we assess people based on them as life realities, then we are talking about what affects us, and we know that very well. So we can avoid judging people (intentions) while being able to filter people out for being the conduits and figureheads of untrustworthy life realities.
Jesus says not to judge. I don't know that assessing someone as untrustworthy is never one of the things Jesus cautions against when he says not to judge. But it seems like we do have to filter people out of our lives sometimes, and do so because we have some reason that we are aware of. If that counts as judging, then a more minimalist judging (as untrustworthy rather than ill-willed + untrustworthy) seems best.
The good that people do us produces the sense that it is trustworthy, because it is trustworthy. But there can be a kind of "deceptive trustworthiness" (in parallel with deceptive truth), when the good that people do us sets us up to be betrayed later or on a higher level.
All of these ways in which we can come to have a sense that someone else is trustworthy, beyond what is warranted, are natural, and we don't necessarily know in advance the difference between (on the one hand) 1) trusting people because we need them, and it's fine, 2) coming to believe someone has good intentions, and they do, and it's good to trust them for it, and 3) someone does something genuinely good to us in itself, and nothing bad will come of it; and (on the other hand) the darker scenarios discussed above. When you enter into a relationship, how can you know how things will turn out? It wouldn't be worthwhile to never trust anyone.
However, the above insights may be helpful in dealing with people who are no longer in your life, or whom you already have reason to not trust, to help you disentangle yourself from the bonds of unworthy trust. Also, if you find yourself trying really hard to 1) provide for other people's needs, 2) establish that you have good intentions, or 3) do good things for them or to them, you may be working beyond the limit of your abilities, or of your trustworthiness, and you should reconsider what you're doing and perhaps reconsider being in the relationship you're in.