What is the Catholic interpretation of 1 Timothy 4:3 if it is not referring to the Catholic church?
Not at all; commentaries suggest that forbidding people to marry seems to have been part of the dualistic principles apparent among the Gnostic heresy. St. Paul objects to such prohibitions when they are the outcome of false principles which would regard marriage and certain foods as impure. But he has no objection to abstaining from marriage or to fasting when properly understood and based on sound principles (1 Cor 7:8 ff.; 2 Cor 6 :5; 11:24; 1 Cor 9:27) The Church bids us to fast and abstain—not because she regards certain foods as evil, but to help us to mortify our appetites to conquer self so to make spiritual progress.
Fr. Vincent Serpa, O.P.