The word "testify" is sprinkled all through the Gospel of John. John the Baptist testifies, Jesus testifies, the Father testifies, Jesus' works testify, the beloved disciple witnesses the blood and water from the side of Jesus on the cross and testifies about that, and his testimony is true.
But science depends on testimony. When a scientist in a laboratory observes the results of an experiment, that scientist puts the observation into words, or perhaps into mathematical formulations of what has been observed. Other scientists have to depend on the truthfulness of the observer's witness. Occasionally an observer lies and is discovered. The observer has committed the unforgivable sin in science: falsifying observations. That scientist's reputation is ruined.
Scientists are expected to disclose the sources of their funding when they publish the results of their research, because it is always possible that their testimony may be biased in favor of the people who are paying their bills.
Thus even science depends on human witness. What distinguishes scientific observation from other human observation is the expectation that other observers are able to repeat the observation process and hopefully describe their observations the same way as the original observer. Scientific statements must be replicable. But all scientists are human beings testifying to what they experience when they observe their instruments.
Science is a massive operation of millions of people observing and testifying to what they observe. How is that different from millions of people observing phenomena in their spiritual lives and testifying to what they have experienced?
Religious experiences are replicable, not on an individual basis, but on a larger scale, across time. The fact that millions of people gather for religious rituals is evidence that something replicable is going on. This is the basis for the field called "sociology of religion." Scientists in that field do not judge the truth of the stories that people tell--they do not judge the statement that Jesus Christ rose from the dead. They observe the behavior of people who make such statements.
Of course there are millions of people who do not claim to have spiritual experiences. That does not invalidate the testimony of the people who do have such experiences. There are millions of people who report that they get enjoyment from listening to music. The fact that there are millions of people who do not enjoy music--who are not "musically inclined"--is not evidence that music is valueless.
Religious people turn off a lot of other people by behavior that other people judge as foolish. There are religious sects that promote handling poisonous snakes on the basis of a statement in the Gospel of Mark. We think such behavior is unwise and leads to harmful consequences, but that does not mean that people who attend Mass are behaving unwisely. There are scientists who use science for bad purposes, or who conduct their research in harmful ways. The Nazi scientists who performed experiments that caused people's deaths, or the research on syphilis done at Tuskegee have not caused us to judge all research as harmful.
Postmodern theory is correct in claiming that no statements are absolutely verifiable. They are correct in claiming that statements of truth can mask desires to control. I can accept the truthfulness of postmodern theory without concluding that making truth statements is worthless or harmful. To reject all truth statements is to repeat the ancient riddle: "All statements are false, including this one."