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Luther did not recant.
From: John Alfred Faulkner, "Luther and the Bigamous Marriage of Philip of Hesse, The American Journal of Theology Vol. 17, No. 2 (Apr., 1913), pp. 206-231 (on pp. 228-9) -
Whatever occasional regret on account of the scandal Luther may have felt, he never wavered as to the essential right of his course with Philip. In June, 1540, in a letter to his electoral prince (first printed in 1872) he gives his own philosophy of the matter, and before I close the reader ought to see the important parts of this statement:
..." If such a matter as this of Philip's came before me today, I would advise as I have already advised. I am not ashamed of such a counsel, even if it should come before all the world...."
Upvote:3
Here is what Luther said on the matter, a number of years prior to the polygamous marriage of Philip:
I confess that I cannot forbid a person to marry several wives, for it does not contradict the Scripture. If a man wishes to marry more than one wife he should be asked whether he is satisfied in his conscience that he may do so in accordance with the Word of God. In such a case the civil authority has nothing to do in the matter. Letter to Chancellor Gregory Bruck, January 13, 1524 (De Wette II, 459, pp. 329, 330)
In a book about Luther's wife, Katharina Von Bora, it states:
(Luther loved to tease his wife. He said,) "One of these days a man will have more than one wife." Kate resounded, "Only the devil would accept that as true...St. Paul said, 'Each man should have his own wife'" (See 1 Corinthians.) Luther replied, "True, but not "just one.'" Then his wife rejoined, "If that happens I will leave you with all the children and return to the nunnery." (p. 137)
I once read that after the 30 years war the Lutherans in Bavaria allowed men to take multiple wives for a short period of time. I also read that in Germany in 1650 the parliament at NΓΌremberg allowed it. Unfortunately, I can't provide primary source references, other than secondary sources like here and here.
The ELCA branch of the Lutheran church in America allows for gay marriages. But at the present time they are restricted to monogamous relationships. The other branches of the Lutheran church in America, such as the LCMS, LCMC, NALC, WELS, etc., restrict the Christian rite of marriage to just heterosexual unions. At present, the practice of polygamy is discouraged, but technically is an open question, within all branches of Lutheranism in America. That polygamy is currently against the law is the major restraining factor for why it is not practiced. Although, some are trying to adopt variations of it.