As a same-sex partnership hasn't happened within the Royal Families mentioned, no one knows.
How the churches in those countries see such a union is another matter.
For Norway:
religion: Evangelical Lutheran faith (the King must always belong to this faith)
marriage must be with consent of: the King
http://www.unofficialroyalty.com/norwegian-royals/75-succession/348-line-of-succession-to-the-norwegian-throne
For Sweden:
religion: Lutheran (for the King & Princes of the royal family)
marriage must be with consent of: the King with the advice of the Council of Ministers (for Princes & Princesses)
http://www.unofficialroyalty.com/swedish-royals/80-succession/401-line-of-succession-to-the-swedish-throne
For the UK/Commonwealth: the Monarch is Head of the Church of England. Those in the line of succession who wish to marry mush have HM's permission (Royal Marriages Act). If someone in the line of succession marries a Roman Catholic, he or she loses their place in the succession.
http://www.unofficialroyalty.com/british-royals/35-succession/48-scott