Of course every Quaker is entitled to their own beliefs and if you ask 10 Friends a religious question, you may very well receive 10 different answers.
Catholics revere Mary far greater than MOST Quakers.
Catholics believe The Bible is the written word of God and Quakers believe it is simply a tool for inspiration and that one should not spend all day listening to a physical book when you get just go inside of yourself and find God waiting patiently there.
Catholics - priest and deacon & Quakers- no clergy
Catholics- Baptism, Communion, Confirmation & Quakers- No physical sacrament is required.
Catholic Mass- ritual & Quakers- spontaneous, no rehearsed service
Catholic- The world was created exactly how it says in Genesis & Quakers- SOME believe it was created as it was in Genesis, just the Biblical "day" was not 24 hours but many, many centuries. Still other Friends believe differently.
Overall, Catholics are required of many things and must follow a rigid set of beliefs, while Quakers are free to believe what they want on most things.
Improved answer:
While Catholics may believe the word for word description of creation in Genesis, they are not required to believe it literally. God created the Universe but was free to create it in any way he wished and did not necessarily follow the human description in the Bible.
Catholics have seven sacraments, not four.
Catholics may not always agree with the Church's teachings but it is better to have moral guidance on how to live our lives rather than everyone doing his/her own thing. That causes pandemonium.
The religious groups included the Protestant, Quakers, Anglicans, and French Huguenots, and some Catholics.
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The Church of England and also other Protestant groups, probably some were also Roman Catholics. I know at least one Jew who has become a Quaker.
Quakers first major colony was Pennsylvania, Quakers did settle in this place but not too long. Next colonies were West Jersey and North Carolina they settle for some time in North Carolina but a war arises between French and Quakers and the Quakers lost that battle.
The main difference is the authority of the pope. Catholics accept it, Protestants and Orthodox don't. There are some differences in the cannon (list of books) included in the Old Testament (although they all have the same New Testament). There are several different types of Protestant religions (Lutheran, Methodist, Anglican, etc) which have differences between themselves and differences between Catholic/Orthodox. So complicated to get into more specifics.
The first difference is probably that Roman Catholics are lead by and believe in the Divine authority of the Pope while Protestants do not accept the authority or infallibility of the Bishop of Rome.
Some of them were coming over to find religious freedom, like the Quakers, while others sought economic opportunities in the New World.
Mostly Catholics and Quakers
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No Quakers don't take communion.
The simple answer is that, when it is necessary to group religions, Quakers are generally counted as Protestants. A more complex answer is that there are many definitions of what it means to be a Quaker and what it means to be a Protestant. Some would say that there are enough differences in belief that the groups should not be lumped together.