Hello, everyone, I freely admit that I have never cast a spell, although I do believe in magic. The Bible does describe multiple acts of sorcery. While I do wish to learn how to do magic myself, I am still a staunch Christian. Is there a way to do magic without praying to gods who aren't Jesus?
I think the most common amalgam is a combination of Christian spiritualism (structure/hierarchy) with wiccan-inspired process replacing standard prayer.
For example casting a circle to create a sacred space under the light of God, calling on the archangels (like Michael, Gabriel, Raphael, or Jophiel) to stand the corners. Or using magical rites to ask for the presence, protection, or guidance/wisdom of one of the heavenly host. I think of it as an act of physicalizing prayer. Instead of sitting and quietly asking for an angel to help you find love (as an example) you are putting attention to symbols of love. Actively blessing them. Placing them in a place you can see. And being reminded of your desire and efforts towards it every time you look upon them.
Magic ritual is effectively structured prayer, a tool to bring focus, effort, and intent towards a specific goal through tangible symbols. Who a person prays to during that working is a matter of their individual philosophies and callings.
Perhaps one other thing to note as well. One does not need to work magic to walk a magical path. Just as it is not prayer that makes someone a Christian, it is not magic that makes a person a witch. There are Christians who hardly pray but read the Bible and believe in it. There are also witches who study the wheel of the year or follow the phases of the sun and moon and stars but hardly work magic.
Prayer is something a Christian does yes, but it is the person's -belief- in and -connection- to the philosophies, ideas, morals, and representations specific to Christianity that defines it. Belief in a singular God above all. Belief in heaven (and hell) as afterlife. Believing in (and learning from) the stories of Jesus and the apostles within the Bible. Using all of that to explore your nature and purpose as a human and as a spiritual being. Prayer is not the root of faith, just one expression of it.
It is likewise for the many magical paths out there. The gods/pantheons people follow. The morals of their personalities and representations. The stories told about and around them. Heck, even the cultures they come from all become sources of learning. They provide the emotional connection and inspiration to explore the same things. Our nature as humans, our roles in (and responsibilities to) the world, to eachother, and to ourselves. None of that comes from magic. Magic is something a person does through/because of it.
In the end you can certainly be Christian, and you can still work magic without violating your faith. It lies in understanding magic as a thing being done through your faith. You are physicalizing and ritualizing an expression of your faith.
How do you think things like the Lord's prayer came about? It isn't just a few colorful words to say. It is a formula and structure very similar to a magical statement within ritual. Seriously, the lord's prayer is a lesson on how to structure any other prayer, and follows an effectively simple magical formula. Use the structure of the lord's prayer with understanding and towards specific intent, and you are working magic. (Not to mention other full-on actual rituals like the lesser banishing or lesser exorcism. Those are already magics. Done and sanctioned within Christianity for quite a long time.)
I'd like to add that Witchcraft is a secular practice. This means that there's no religion tied into witchcraft inherently. Though one can certainly add it if they want. There are also no inherent Gods in witchcraft, though of course if someone wants to work with Gods, it is their choice. Additionally, in witchcraft one works with a God the same way a witch works with a spirit. It's very much a give and take relationship where your an equal to them so your work matters as much as there's. Of course I don't want to info dump on you but I just thought I'd add that. Since you asked "Is there a way to do magic without praying to gods who aren't Jesus?"because a lot of the early 1950's books on witchcraft would mix up terms like Witchcraft and Wicca and use them interchangeably, which isn't correct.
One can choose not to incorporate deity or deities into their craft or practice if they want to keep it separate from their religion as witchcraft or the craft is not tied to any specific religion. Many religions use aspects of magic or the craft in their rituals and daily practices. Many religions limit who is allowed to do this type of energy work or lead in a group setting.
There are Christian witches who only incorporate Jesus or other biblical figures into their magical workings. It is purely the practitioners' choice in this matter as to who or what they raise energy and work with to manifest desired results. There are also others, like myself who work with many different pantheons and Christian figures are included particularly when a working or prayer is for a loved one whom is Christian.