How about this for a wild ass, crazy fukkin idea.
Instead of having the term 'marriage' used as a legal term for taxes, benefits, insurance, etc- change it to 'Partner', 'Co-habitant', 'Significant Other', whatever..... to signify two people who are sharing living quarters and expenses. This will also cover hetero couples that do not wish to 'marry' in the religious sense.
Since the basis for this is to be able to claim the same benefits as a 'church-wed' couple, this would allow those outside the cultural norm get a fair shake without blasphemy.
Part of it would require a legal document of co-habitation, so that if they decide to split they would face the same legal and financial responsibilities of a traditional married couple.