Christianity and Wicca as a syncretic, hyphenate religion cannot exist. While there those who very sincerely believe that they are following both, they are not...
The fault rests on how one defines Christian.
If you define Christian as one who believes Christ existed, regardless of whether or not one believes in his teaching, it is possible that one could define oneself as a Wiccan Christian, but most Christians would say, quite rightly, that merely believing Christ EXISTED is NOT what makes a Christian.
Merriam Webster (m-w.com) defines a Christian as " one who professes belief in the teachings of Jesus Christ*"
It is possible to PROFESS belief in the teachings of Jesus Christ and be a Wiccan.
..You'd also be a liar.
Because it is impossible to BELIEVE IN or AGREE WITH those teachings as a Wiccan.
One common teaching in Christianity that is used to define Christianity is the Nicene Creed. If we examine it, we can see it is ABSOLUTELY NOT COMPATIBLE WITH WICCA. Observe.
(My comments follow in brackets:)
The Nicene Creed:**
We believe in one God, [Wiccans are polytheists]
the Father, the Almighty,[Wicca does not teach omnipotence]
maker of heaven and earth,
of all that is, seen and unseen.
[Wicca does not support Creationism but instead teaches "as above, so below, which includes the idea that the Universe may be interpreted by observation of its parts]
We believe in one Lord, Jesus Christ,
the only Son of God,
eternally begotten of the Father,
God from God, Light from Light,
true God from true God,
begotten, not made,
of one Being with the Father.
[Wicca teaches that there are multiple gods, and that all people are children of gods. Wicca does not mention Jesus at all.]
Through him all things were made.
[Wicca teaches that humankind makes many things.]
For us and for our salvation
[Wicca has no concept of salvation]
he came down from heaven:
by the power of the Holy Spirit
[Wicca has no heaven, nor a Holy Spirit]
he became incarnate from the Virgin Mary,
and was made man.
[Wicca teaches that humans are born human and gods are born gods. Transformation in one life from one species to another is not a part of Wicca.]
For our sake he was crucified under Pontius Pilate;
he suffered death and was buried.
[HUGE POINT! Wicca teaches that RESPONSIBILITY for all of a Wiccan's actions are upon that Wiccan, and must be taken care of by that Wiccan. Thus, in Wicca, it is impossible to die or suffer for someone ELSE except in very specific, personal situations (like taking a bullet for someone.) Wicca teaches there are no SINS, so there was literally no reason for Christ to die!]
On the third day he rose again
in accordance with the Scriptures;
[This is in no WICCAN Scripture]
he ascended into heaven
and is seated at the right hand of the Father.
[Wicca has no concept of who sits to what side of any father deity.]
He will come again in glory to judge the living and the dead,
and his kingdom will have no end. [Wicca has no teaching about a half-god judging living or dead, and, in fact, has teachings about who judges the dead...There is also no teaching of a Kingdom to Come in Wicca.]
We believe in the Holy Spirit, the Lord, the giver of life,
who proceeds from the Father and the Son.
[And Wiccans don't]
With the Father and the Son he is worshiped and glorified.
[Which Wiccans don't do.]
He has spoken through the Prophets.
[Who are not Wiccan.]
We believe in one holy catholic and apostolic Church.
[Which Wiccans do not.]
We acknowledge one baptism for the forgiveness of sins.
[Wiccans neither baptize nor sin.]
We look for the resurrection of the dead,
[Wiccans do not.]
and the life of the world to come.
[Wicca does not teach of a coming future world, but of NOW worlds.]
I am sure there are some who think they are Wiccan and Christian, but they aren't. Either you think Jesus died for your sins (Christianity) or you acknowledge the doctrine of Self-responsibility as a proper person or adult human (Wicca). They are mutually self-exclusive.
I actually feel sorry for those that do think they are one and the same because every one of them I have met confuses Wicca (Worship of the gods and living by their standards) with magic, and Christianity has a long and perfectly valid tradition of magic that existed BEFORE WICCA ever existed. Here are some books discussing it:
The Magical Writings of Thomas Vaughan:
Greater Key of Solomon:
Ancient Christian Magic:
The Divine Synthesis and Realization of Magic by the Christian Revelation
"Christian Wiccans" either have Christianity all wrong or have Wicca all wrong, and that's sad. Many have also been unfairly persecuted, and judge all who oppose their claims as discriminating or being mean when, in fact, they are trying to help.
*There are other definitions, but they are specific to sects of Christianity