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I believe that from a technical standpoint she would have no obligation to uphold Catholic teaching. However from a Catholic perspective on marriage it would seem incompatible that a Catholic man would be married to a non-Catholic woman who used birth control which is in direct opposition to the Church’s teaching. In the Catholic Church a married couple is united as one entity. For the non-practicing/non-believing spouse to act in a manner contrary to Church teachings is incongruent with the idea of unity within a marriage. While not “illegal” it would certainly seem incompatible and therefore a potential area of strain within the marriage.