Makes me feel very odd indeed but I do agree:
I would outlaw marriage for everyone, including heterosexuals, and grant access to a civil partnership union across the board.
This is the situation in, just as an example, Portugal. In a legal sense there is no such thing as marriage. There is just the single civil partnership thing for all potential mixtures of two people (they are traditionalist enough still to insist upon that) who wish to sign up to the contract.
Of course, it\’s possible to refer to this as marriage if you wish to. But what, in the terms Bindel is using at least, we normally describe as marriage has no legal weight here. You want to go to church, synagogue, mosque, the local gun club or get the publican in to run a ceremony for you? Sure, go right ahead. As far as the law is concerned you\’re entirely free to do that just as the law is entirely free to ignore that you have done so. Which many people do and the law does.