Just to point out that the action depends on whether or not the Protestant is baptized or not baptized.
In the case of a baptized non-Catholic, permission is needed as so far described for the legal marriage of such a person to a Catholic. Canon 1124 only mentions a “competent authority,” but in context this would be the diocesan bishop, the local ordinary, or someone whom either might delegate.
If the person is not baptized, then a dispensation from the impediment of disparity of cult (c. 1086 §1) is needed for validity. This can be given only after the cautiones of canon 1125 and whatever the episcopal conference has required have been taken care of. As well, canons 1127 and 1128 would additionally apply (see canon 1129 which mentions this).
According to canon 87 §1, a diocesan bishop can give a dispensation from such a universal disciplinary law, as as that of canon 1086 §1) as often as he judges that it will contribute to the spiritual good of the faithful. The local ordinary has the power of dispensing this impediment and certain others according to canon 1078§1.
Only a just and reasonable cause is mentioned in canon 1125, so spiritual advantage does seem to suffice. Nothing prevents a bishop from setting down some criteria for how he would determine the spiritual good of the faithful or to give an indication of just and reasonable cause. Some of the criteria that a bishop might use to specify this further might include the promised or founded hope of the conversion of the non Catholic, the promotion of family harmony, danger of a marriage before a non-Catholic minister if the permission or dispensation is not given.