I would say that there are many reasons it is important to study the psychology of religion. First, if you are studying religion or people, then you need to know something of how they think. This can give you invaluable information. This point alone makes such a study worthy it.
Second, if you are studying why certain people gravitate towards one religion and not another, there might be a psychological component. To study this can be helpful to chart the growth of religions or even to create a model to predict growth.
Third, some religions may seek to manipulate people's minds, especially some very odd cults. If you recall Jim Jones and his cult movement (Peoples Temple), it was a huge disaster and tragedy. Over nine hundred people committed mass suicide. Hence, to study the psychology of religion would be very important.
This is a good question because in the present world we need try to study it. In the past people were ignorant but those who interpreted the books related to the religions, they talked about Hell, Heaven, Jannat, Dojak etc and spead fear amomg the masses of of severe punishment if they disobeyed the teachings.
For example, in Hindu, the upper caste Brahman only were authorised to learn Vedas and perform the rituals. They always told people not to read the scriptures because they knew it very well that their lies will be disclosed. So people were very scared of doing that. People were very rigid to the bindings told by them. They exploited the masses in the name of religion and as a result Buddha religion came into being which does not believe in God but Knowledge first.
By and large people became educated and learnt everything. Still there are some people who motivates the ignorant who have not gone inside these books and become prey to these people becoming disciples and abiding by the teachings. These lead to clash between believers of different cults.
In the same way, in other religions also, the same thing happened and yet happens. It is difficult to talk or even interpret according to our understanding. They feel insulted and become ready to kill each other.
Therefore it is very important to study the psychology of every religion and if possibe to bring out possible accepting interpretation to lead the people in the right path to make our earth a place of peace and harmony.