No the Mortgage interest deduction would not be unconstitutional. DOMA was the government restricting benefits to a distinct group and violating equal protection. The judicial precedent for equal protection for federal laws is somewhat fuzzy as there is not equal protection clause specifically written as part of the fifth amendment, and the specific clause is only in reference to states in the fourteenth amendment.
This is how the precedent has been set for federal equal protection under the fifth amendment:
By [the 14th amendment's] terms, the clause restrains only state governments. However, the Fifth Amendment's due process guarantee, beginning with Bolling v. Sharpe (1954), has been interpreted as imposing some of the same restrictions on the federal government: "Though the Fifth Amendment does not contain an equal protection clause, as does the Fourteenth Amendment which applies only to the States, the concepts of equal protection and due process are not mutually exclusive.
In the case of a religious person not getting a mortgage, that decision is made by that person alone and the federal government is not forcing them to get one or denying them the deduction should they claim it with a valid mortgage because they also claim X belief. Windsor was actively denied a benefit given to others by the federal government, the hypothetical religious person is not denied anything by the government but by their own choice. Furthermore a person paying cash for a house may pay more tax, but they are paying less for the house so the are in effect paying "interest" to the government, while those who borrow pay interest to a bank.
This ruling is based on the states rights to define a marriage which is legal being in conflict with the definition in DOMA, the definition for DOMA was found unconstitutional based on equal protection under the fifth amendment.
When the State used its historic and essential authority to define the marital relation in this way, its role and its power in making the decision enhanced the recognition, dignity, and protection of the class in their own community. DOMA, because of its reach and extent, departs from this history and tradition of reliance on state law to define marriage. Discriminations of an unusual character especially suggest careful consideration to determine whether they are obnoxious to the constitutional provision.
For same-sex couples who wished to be married, the State acted to give their lawful conduct a lawful status. This status is a far-reaching legal acknowledgment of the intimate relationship between two people, a relationship deemed by the State worthy of dignity in the community equal with all other marriages. It reflects both the community’s considered perspective on the historical roots of the institution of marriage and its evolving understanding of the meaning of equality.
DOMA’s unusual deviation from the usual tradition of recognizing and accepting state definitions of marriage here operates to deprive same-sex couples of the benefits and responsibilities that come with the federal recognition of their marriages. This is strong evidence of a law having the purpose and effect of disapproval of that class. The avowed purpose and practical effect of the law here in question are to impose a disadvantage, a separate status, and so a stigma upon all who enter into same-sex marriages made lawful by the unquestioned authority of the States.
The federal statute is invalid, for no legitimate purpose overcomes the purpose and effect to disparage and to injure those whom the State, by its marriage laws, sought to protect in personhood and dignity. By seeking to displace this protection and treating those persons as living in marriages less respected than others, the federal statute is in violation of the Fifth Amendment. This opinion and its holding are confined to those lawful marriages.