Which is more conservative, a t test or a Z test?

Answer 1

each stat has its own criteria; both are equally "conservative".
Since the criteria for the application of each is statistically significantly discernible-you know, "different"- , you would not be using them with the same set(s) of data....

overall, the "z" is more general, in that there is no consideration for the degrees of freedom; in that regard, the student t test could be more restrictive, depending on the sample set..degrees of freedom...