According to my understanding of the relevant Canon Laws (1108 and 1124- about 1129)
1) A Catholic can marry a baptized Non-Catholic (Protestant)only with a dispensation from the Ordinary (Bishop)note: A Priest can NOT grant a dispensation.
2) A Catholic can marry a Non- Christian (unbaptized, Jew, Muslim, Hindu, Buddhist etc) only with a dispensation from Rome. note: The local Bishop can NOT grant a dispensation for Non-Christian marriages.
3) A Catholic can get married in a Protestant parish (or anyWHERE outside a Catholic parish, yet the vows (promises) can only be voiced to a Catholic priest and the priest must be the one that ask for the promises (ie “Do you John take...)
4) If the Catholic in any way knowingly avoids these “laws” (one which includes getting “married” by a Justice of the Peace) they have incurred excommunication
It may seem harsh, yet there are good valid reasons for these Church laws. Rogue priests have ignored these laws at the expense of many Catholics.