There are plenty of rational ways to do that. I'm guessing you'd primarily disagree with the axioms on which they're founded.
How about "state recognition of marriage is primarily about supporting the family unit as the nucleus of society - as same-sex union can't create children, long-term partnerships engendering opposite-sex union are to be promoted in order create a general impetus towards stable home environments for child rearing and raising". That seems rational; disregarding verity do you disagree it's rational?
If you argue against this definition then to my mind you come to define a new relationship, let's call it civil-union. In civil-union there seems no logical reason to exclude same-family, or multiple-person unions. I can't see how you can say "the definition of marriage as the union of a man and woman [who're not closely related]" is wrong because it limits marriage to a particular historical/tradition form and then come up with a new definition to foist on people that excludes groups (families, polyamorous, etc.) for arbitrary reasons that don't even have the support of history or tradition [or theology].
>Probably the closest modern issue is [...] //
So are you saying if a CEO of a company believed euthanasia to be wrong you'd stop using that companies products?