The problem is as the Ecumenical documents warn, we do not create unity where it does not exist by sharing Sacraments.
A Catholic of course cannot stand up and say they will help the parents raise the child Methodist.
The Methodists of course would not like it if they stood up and professed to help the parents raise the child Catholic:shrug:
Disclaimer: First of all, I am in no way saying that any Catholic should go ahead & do this, if the Catholic Church says that you should not. You need to follow the rules of your faith, not someone else’s.
OK, that said, as the

Friendly Neighborhood Methodist, I need to point out something in Br Rich’s post, quoted above:
The godparents at a Methodist baptism **will not **be asked to say that they will help to raise the child as a Methodist.
They will be asked to agree to raise the child as a
Christian. And since Methodists recognize Catholics as our brothers & sisters in Christ,
that promise would be more than adequately fulfilled by a godparent who, in the event of need, should even himself/herself actually raise the child as Catholic.
Now, this may still not meet the requirements of the Catholic Church, and I do not want to be seen as encouraging anyone to fly in the face of the requirements for a faithful Catholic. It is very possible that inter-religious godparents may be something that Catholics are not allowed to be, in which case, the appropriate thing to do is to decline on the grounds that you are not allowed to participate.
I am just saying, that if this is the only objection, that I did want to say, that the Methodist baptismal ceremony will not require any person to make a promise that would involve raising a child specifically as Methodist.
Indeed, so far as I understand the difference, Methodist godparents’ role is closer to that of “Christian witness” than to godparent as defined by the Catholic Church.
But,
please, don’t run out & do something because I said this!!
I just wanted to point out a difference in the 2 ceremonies that I did not see in Br Rich’s answer.*** Not***

foment rebellion!!:nope:
PS: All of this applies to
United Methodists, my own faith tradition. I have no information about the ceremony in other churches that may fall under the broad category of “Methodist”.