True and mutable is one of the wisest phrases I know. It means we should hold our best explanations true and act on them, not give in to relativism. Just because we may be wrong, does not mean any particular idea we have is wrong, or that we should not hold our ideas true. It also means that our ideas must be mutable -- they must be open to criticism and change and improvement. And being mutable does not make them less true.
When someone says something is true, s/he does not mean s/he's certain it is true. That, of course, would be absurd. So what does it mean to assert something is true? Simply that it is the best explanation.
There is a common fallacy that says fallibilism implies mistakes. The logic is that because we can't be certain, we are bound to make mistakes. The refutation is to look at a particular action or theory, and point out that, while it may be a mistake, fallibilism does not state it is, and all we can do is use our best explanations. So, fallibilism is not an argument against this specific thing. Then, we examine another action/theory. Then another. The point is, fallibilism does not imply any particular mistake, and cannot be used as an argument against the truth of any particular proposition.
Credit for the phrase true and mutable goes to Yehudit's LGF comment here.