The below is an answer from the Roman Catholic perspective.
The Church's outreach to the Society of Friends would fall under Ecumenism and Interreligious Dialogue of which His Holiness, Pope Benedict XVI, is a big supporter;
Pope Benedict XVI has reaffirmed the commitment of the Catholic Church to the ecumenical movement, and stated that ecumenism would be the "primacy task" of his pontificate. This is an excerpt from his address to the Cardinals at the end of a Mass he celebrated with them the day after his election, on Apr. 20, 2005:
Nourished and sustained by the Eucharist, Catholics cannot but feel encouraged to strive for the full unity for which Christ expressed so ardent a hope in the Upper Room. The Successor of Peter knows that he must make himself especially responsible for his Divine Master's supreme aspiration. Indeed, he is entrusted with the task of strengthening his brethren (cf. Lk 22:32).
With full awareness, therefore, at the beginning of his ministry in the Church of Rome which Peter bathed in his blood, Peter's current Successor takes on as his task the duty to work tirelessly to rebuild the full and visible unity of all Christ's followers. This is his ambition, his impelling duty. He is aware that good intentions do not suffice for this. Concrete gestures that enter hearts and stir consciences are essential, inspiring in everyone their inner conversion that is the prerequisite for all ecumenical progress.
The puritans wanted to purify the catholic church of the Quakers
The catholic church still teaches transubstantiation.
Counter-Reformation
In the Catholic church, the priest will ask "what do you ask of God's church for your child?" The response is "Baptism"
Sarah R Wagner has written: 'Architecture as a response to today's Catholic Church' -- subject(s): Church architecture, Catholic church buildings
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The Catholic Counter-Reformation was in response to the Protestant Reformation. Its goal was to reform the Catholic Church from within.
The Protestant Reformation :)
If the question refers to the location of, or description of, a church, or its denomination, then the response, 'The church is ... ' is correct. If the questions is about a church as a specific entity, the word 'church' should be capitalized. For example:'Where is the church?': 'The church is two blocks away.''Where is the Catholic church?': 'The Catholic church is in the next street.''What is the church built of?': 'The church is built of stone.''How old is the Christian Church?': 'The Church is over two thousand years old.'A devout believer in a particular religion, asked 'Why does your Church exist?' might respons simply, 'The Church is.'
Because the Quakers didn't approve of the Anglican Church. The Anglican Church was basically the Church of England. The Vestry Acts collected money for the Anglican Church so the Quakers didn't want to.
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Catholics settled the colony of Maryland to escape the persecution in England. England had become anti-Catholic after King Henry VIII broke with the Catholic Church to establish his own church.