The Netherlands were of course one of the first European countries to recognize same-sex marriage rights but to my knowledge, no one there has ever made a serious move towards corresponding same-sex marriage rites. Long before the Dutch government recognized same-sex marriages, they distinguished between marriages recognized by the state and marriages recognized by the church. Linguistically, it's kind of a rights vs rites distinction. The Dutch words are burgerlijk huwelijk for civil marriage and kerkelijk huwelijk for church marriage.
It's important to recognize that those terms predate the acceptance of same-sex marriage in that country by decades. When the time came to broaden the meaning of burgerlijk huwelijk to include same-sex couples, there was no corresponding need to broaden the meaning of kerkelijk huwelijk. I am unsure what religious freedom the Dutch people enjoy, but judging from the protections granted to Muslims I'd guess that they're pretty broad.
The linguistic situation in this country is more nuanced. Claimants for the word "marriage" to cover same-sex unions are insensitive to other's rites while claimants to the word "marriage" to exclude same-sex unions are insensitive to other's rights. I'm not sure there is any easy way to resolve this.