Physicists tend to be interested in parapsychology because of the implication that we have a gross misunderstanding about space and time and the transmission of energy and information.
Biologists are interested because psi implies the existence of additional, unexplained methods of sensing the world.
Psychologists are interested for what psi implies about the nature of perception and memory.
Philosophers are interested because psi phenomena specifically address many age-old philosophical problems, including the role of the mind in the physical world, and the nature of the objective vs. the subjective.
Theologians and the general public tend to be interested because personal psi experiences are often accompanied by feelings of profound, ineffable meaning. As a result, psi is thought by some to have "spiritual" implications.
From the materialistic perspective, one of the foundations of the current scientific worldview, human consciousness is nothing but an emergent product of the functioning of Brain, Body, and Nervous System (BBNS). That is, no matter how different mind may seem from solid stuff like bodies, it is generated solely by the electrochemical functioning of the BBNS, and so it is absolutely dependent on it. When the BBNS dies, so does consciousness. From this perspective, claims of survival of bodily death, or ghosts, or apparitions, must be due to wishful thinking. Furthermore, the limits of material functioning automatically determine the ultimate limits of mental functioning, thus ESP and PK appear to be impossible, given our current understanding about how the world works.
And yet, psi phenomena have occurred in all cultures throughout history, they continue to occur, and some of the reported phenomena have been persuasively verified using scientific methods. Because psi seems to transcend the assumed limits of material functioning, and therefore the BBNS, some interpret psi as supporting the idea that there is something more to mind than just the BBNS, that there is some sort of "soul," or the like.
This "non-physical" aspect, an aspect that does not seem to be as tightly bounded by space or time as present scientific models require, might survive bodily death. If so, there may be important truths contained in some spiritual ideas and practices. Of course, parapsychology is a very long way from being able to say that "the data shows that X" (insert your favorite religious group here) are specifically right about religious doctrines A, B, and C but dead wrong about dogmas P, Q and R.
We must emphasize that there is a big difference between simply noting that the findings of parapsychology may have implications for spiritual concepts, versus the idea that parapsychologists are driven by some hidden spiritual agenda. Some critics of parapsychology seem to believe that all parapsychologists have hidden religious motives, and that they are really out to prove the existence of the soul. This is no more true than claiming that all chemists really harbor secret ambitions about alchemy, and thus their real agenda is to transmute mercury into gold. The reasons why serious investigators are drawn to any discipline are as diverse as their backgrounds.