I wouldn't argue with the political leaning of some Danish MPs but the marriage laws in Denmark don't say that.
I think that you are mistaking the legislation on "registered partnerships" with marriage laws. In 1989 Denmark became the first country in the world to introduce a law on registered partnership for two persons of the same sex (Act 372 of 7 June 1989, in force as of 1 October 1989). The law enables two persons of the same sex to register their partnership and gives them (with some exceptions) the same rights and responsibilities as a heterosexual married couple.
The exceptions are: a registered couple cannot adopt children, church weddings are impossible, and one of the partners in a registered partnership must be a Danish citizen and live in Denmark. Apart from these exceptions, the conditions are exactly the same as for heterosexual marriage. The wedding is the same as for civil marriage and the divorce regulations are the same, too.
The law is not valid outside Denmark, so the condition that one of the partners must live in Denmark is obviously relevant. The condition regarding citizenship was not in the original bill, but was introduced during parliamentary debate at the initiative of the right-wing Progress Party. The Danish government recently announced, in a communication with the National Danish Organisation for Gays and Lesbians (LBL), that it will put forward an amendment to the partnership law in autumn 1998 to change the provision on citizenship to stipulate citizenship either of Denmark or of a country having similar legislation. Furthermore, the Minister of Justice has promised to consider to propose that the provision is changed from "citizenship and residence in Denmark" to "citizenship or residence in Denmark".
So, far from it being a prohibitive and xenophobic piece of legislation, it was liberal (in the sense it which it is used in the UK).
According to article 9 (1) of the Aliens Act, a residence permit will be issued to any foreigner living with a person permanently residing in Denmark in a "cohabitation of prolonged duration" of at least two years. This is not required for registered partners, one of whom, as mentioned above, however has to have Danish citizenship.