In Frankenstein how does religion influence Shelley and what she wrote in the novel?
This is a great question and one that is complex. Differences of opinion will exist.
On one hand, Shelley cannot get rid of Christian theology. This is the air she breathes. So, even if there is very little "religion" in her book, her narrative is very similar to the Bible. Like God, Frankenstein creates. He is likened to a father (again like the Bible), and the creature he creates longs for a companion, like Adam, even if Frankenstein denies the request of a companion. Themes of creation, divine paternity, and the importance of companionship emerge, just like Genesis 1-3. Hence, we can say that religion influences the important contours of the book.
On the other hand, as the story progresses, there is very little in terms of religion, especially explicit religion. However, we do see morality. Frankenstein at his death bed regrets not being a better creator/father and the creature confesses his wrongful actions toward humanity. In light of this, these characters come to humane points apart from organized religion. It seems that Shelley is intimating that we do not need religion to get to the best of humanity.
That said, these humane qualities, from another perspective, can be seen as common virtues of religion. In this sense, we can say that Shelley wants the virtues of religion without religion. Is this possible? The reader must decide.