Do you have an actual argument other than two nations that agree with your stance and one that no longer does?
What is the actual reason to not want people have religious marriages, if it's understood that these are not legally recognized? I really don't see it.
Is that understood? I wouldn't want to count the people who don't understand that. I wouldn't even want to count the ministers who don't understand that - e.g.,in Holland many imams are flown in directly from Morocco or other ME countries who don't know the Dutch language, Dutch culture etc., so why would they know Dutch law? - and that's probably the case in other countries too.
Secondly, any religious marriage uses the same vocabulary as a secular marriage. It doesn't say the partners are "religiously married", no, they're "married", they're "husband and wife", and the minister says they have certain obligations towards each other.
The minister doesn't start with a disclaimer "This is only a religious marriage and is null and void for the law. You may disregard all the vows you take here, the police won't come after you, only your neighbors will try to make life a living hell for you if you do so".
In fact, most Abrahamic religions don't even recognize secular marriage, and pretend theirs is the only relevant one. Catholic doctrine is very pronounced in this. AFAIK, only mainstream protestantism is the only religion which consciously says that marriage is the state's business (both Luther and Calvin have explicitly said so).
So yes, I think the State has a legitimate interest in protecting what is sold under the title of "marriage". It does so for a lot of other things, after all.
The State also says that "homeopathic medicine" may not contain health claims that have not been scientifically proved. Or any medicine at all, for that matter, and if you don't disclose the risks properly or try to sell it off-label, you risk a hefty fine.
The State also says that you may only label a product "chocolate" if it has a certain minimum amount of chocolate in it. And not just chocolate, about any food product has been regulated as to its contents.
In the same vein, the State may regulate what's being sold as "marriage". As it's actually the monopolist (in continental Europe) in selling marriages, it also has a legitimate interest in regulating what's being sold by religions as a marriage and to whom.