Christian Concern is speaking out after the tree decoration went on sale on UK retailer zazzle.co.uk.
A second ornament shows Jesus with two fathers.
The decorations are being sold for £13.
"The idea of putting a Joseph and a Joseph with the baby Jesus or a Mary and a Mary is blasphemous," Andrea Williams from Christian Concern told Premier. "It strikes at the face of God. It strikes at the heart of the message."
A spokesperson for Zazzle said: "Zazzle is a marketplace of artists and designers who create art and designs to sell on Zazzle. These ornament designs do not violate Zazzle policies and represent the creative expression and viewpoint of the artist who designed them."
According to the Daily Mail, the creator of the decorations is considering removing them from sale "out of respect for fellow human beings".