There was once a time (and still some places) when religion played a role in regulating other aspects of society, like dietary regulations. Nobody says "keep religion out of my kitchen" when the local health department insists that you don't cross contaminate other foods with utensils used on raw meat.

Just because we used to regulate these ideas with religion in the past doesn't mean that our current institutions are religious. Some people who are legally married also subscribe to religious meanings of marriage. Some people who have food handlers cards also follow religious food customs. They're related but independent concepts in the modern day. The modern legal construct of marriage in the US is secular.