Final answer:
The Society of Friends, also known as Quakers, is the religion that allowed women to preach and participate equally in church services, unlike the Puritan Church and the Church of England.
Step-by-step explanation:
The religion that allowed women to preach and speak out during church services among the options provided is the Society of Friends, commonly known as the Quakers. Founded by George Fox in the 1640s, the Society of Friends was quite progressive for its time, promoting the idea that the Holy Spirit could move anyone to speak, regardless of their gender.
This belief effectively gave women the same rights as men within their church gatherings. In contrast, the Puritan Church and the Church of England did not usually permit women to take on such roles in the church. The Society of Friends held that each individual had a direct relationship with God, which allowed them to reject the hierarchical structure of the Church of England.