Can a priest as a matter of personal conscience refuse to marry a Catholic with a non-Catholic? For example perhaps he takes a literal view of the New Testament verse “do not be unevenly yoked with unbelievers.”
The Catholic Church does give dispensations for Catholics to marry members of other Christian churches or of other religions. So a priest cannot refuse a wedding simply for such a reason. A priest may refuse to witness a marriage because he judges one or both parties to be too young or to be lacking in sufficient psychological maturity, etc. However, the example you give regarding Scripture could be true of a Protestant clergyman, but not of a Catholic priest. It is not for the individual Catholic to have his own private interpretation of Scripture apart from that of the Magisterium, the teaching authority of the Church. Further, the priest may refuse to officiate, but he cannot prevent the couple from going to another priest who might have a different pastoral opinion. All things being equal, Catholics have a right to the Sacraments.
Fr. Vincent Serpa, O.P.