I’m absolutely sure it not permitted in my church, and I’m absolutely certain you are correct.
It is not to be done. Verboten! Unsound!
And yet God calls us to kneel together. If we need to use other terms to describe the relationship then you will hear those words, but my heart speaks otherwise.
My pastor knew the Godparents (we call them sponsors) were Catholic and after interviewing them extensively he gave his consent. We recited our vows as parents. They recited the vows to help bring up this child of God in the church and the congregation recited their vows as well. My pastor accepted those vows and the child was baptized in the name of the Father, the Son and the Holy Spirit.
So there it is. It has been done. If there is fault, may I bare it entirely.
I do admit that we don’t talk about it much so as not to cause scandal, but they have been a blessing for my and my children in a life of faith. Frankly, if my child became Catholic, I would be content.
I have three children, and frankly at this time, the only sponsors of my children before God who have bothered to perform their duty are these good Catholics. If I had to do it all over again, all three of my children would be so blessed.