Hi Mayim! Welcome to OBOB and ChristianForums.
As I take it, Catholicism has different orders and rites within it. I know of a couple by memory. But does there exist a Catholic order or rite which is similar to Methodism?
You would be right about the rites (lol).
There are
24 self-governing Churches that make up the Catholic Church, and there are probably around two times as many different rites that have developed over the centuries. Rite, in this sense, refers to a way of expressing the Catholic faith in worship, prayer, and other ways.
There is no rite or church in the Catholic Church as a whole that is associated with Methodism. The closest analogue we have are the
Ordinariates of the Latin Church. They are made up of former Anglicans and Episcopalians (as well as other Protestants) who have joined the Catholic Church. They worship God and pray according to liturgical books that are informed and influenced by the Book of Common Prayer. They believe everything the Catholic Church believes, but they have kept various traditions that originated in the early English church and Protestantism. It's very cool.
Mainly, adhering to iconoclasm and a lack of veneration towards saints.
All of the churches in the Catholic Church profess
iconodulism (veneration of images) and veneration of the saints. It is part of our beliefs as Catholics since it goes back to the early Church and, we believe, has foundations in the Scriptures.
In private devotions though, we are always free to emphasize certain things or not.
I ask because I am flirting with perhaps converting, but these areas are sticking points.
I can relate. I am a revert from the Southern Baptist community, and so veneration of saints and images were stumbling blocks for me.
If you are interested in converting, might I suggest that you take some more time to check out why we believe what we believe about veneration of images and saints? You've probably already done a lot of that (good for you!), but there's a lot of riches in Catholic teaching. Personally, one reason why I came to accept the practice was because I saw how there are Biblical foundations and historical reasons why Catholicism does it.
These resources would be a
great place to get started. Also, I'm sure we'd all be happy to discuss the issues if you would like.
In any case, you are most welcome here! God bless you.