Two baptized Catholics in order to have a sacramental marriage must be married by a Catholic priest/deacon for it to count.
Without it, they are not able to receive sacraments until/unless they have their marriage convalidated in the Catholic church.
Why would anything different apply?
However, if a Catholic wishes to marry a baptized Christian non-Catholic, their marriage can be witnessed by a Christian minister if a dispensation from canonical form is issued by the Catholic church, and the Catholic party signs an agreement to do everything in their power to raise the children Catholic. The Christian party does not have to sign anything.’’
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