Can anyone name a diocese which will enter a SSPX witnessed marriage in its registry? Mine won't.
Then they are gravely derelict in their duty. Even if no harm actually comes, they are guilty of whatever harm COULD come. To give your imagination some help, picture a seminarian who was actually married getting ordained later on. All the evils that would flow from that would be this person's fault.
SSPX marriages are certainly valid. SSPX priests are valid priests, and it's the couple that confects the marriage.
But even if the Conciliar authorities disagree with the Traditionalist position and the justification thereof, they have to admit that a couple is married and go ahead and register them, so they can't get married again, etc.
To do otherwise, they don't have a leg to stand on. Vatican II or no, 1917 Canon Law or 1983 Canon Law. They can't even quote something post-Vatican II that would defend this behavior.
Our SSPX priest certainly sent information about my marriage to my wife's home parish, etc. It's not like my wife is from a super-Trad parish and/or with a traditionally-minded bishop or something. No, they are quite average. But they will certainly record a done deed like a marriage!
We're not talking about being in the "Parish registry", or even on the "good standing" list. That's a different matter. But they need to note that one of their former parishioners has been married, so if that person later tries to get ordained, the seminary will be contacting *that same parish* for the person's records. That's how it works. It's a question of organized, distributed record keeping. It's not some kind of "seal of approval".
Besides, the Conciliar Church is supposed to be super liberal now. They want to allow "civil unions" between ɧoɱosɛҳųαƖs, and virtually bless second marriages after divorce (without annulments) and give them communion.