You are correct that the sacraments are truly mediated by Christ himself in the Holy Spirit “in persona Christi” via the bishop or priest.
In case of emergency “anyone” can administer the sacrament of baptism, but the ordinary is done by a bishop or priest.
You are correct again, that “valid” sacraments remain valid no matter the disposition of the minister or recipient.
When it comes to the Eucharist the Early Church Fathers both East and West teach that no Eucharist is valid unless approved by the bishop or the one whom the bishop has placed this charge.
St. Ignatius of Antioch;
Let all follow the bishop as Jesus Christ did the Father, and the priests as you would the Apostles. Reverence the deacons as you would the command of God. Apart from the bishop,
let no one perform any of the functions that pertain to the Church. Let that Eucharist be held valid which is offered by the bishop or by one to whom the bishop has committed this charge. Wherever the bishop appears, there let the people be;
as wherever Jesus Christ is, there is the Catholic Church. It is not lawful to baptize or give communion without the consent of the bishop…Letter to the Smyrnaeans, Chap. 8
Here is where problems arrive from different communions, because the Catholic Church cannot and will not move from her status as Rock,
revealed from the Didache chapt. 14:1
"And on the Lord’s Day, after you have come together, break bread and offer the Eucharist, having confessed your offenses, so that your sacrifice may be pure.** But let no one who has a quarrel with his neighbor join you until he is reconciled,** lest your sacrifice be defiled…
The Lord said; "In every place and time let there be offered to me a clean sacrifice… Malachi 1:11, 14
A clean “Valid” sacrifice offered to God in the Eucharist is one offered by the Catholic bishop and all those in communion with the bishop.
St. Jerome; "Far be it from me to censure the successors of the apostles, who with holy words consecrate the body of Christ, and who make us Christians. Having the Keys of the Kingdom of heaven, they judge men to some extent before the day of judgement, and guard the chastity of the bride of Christ.
There is much more to expound upon the communion which makes for a clean sacrifice offered to God by unity with the Catholic bishop, reconciliation must be reached first and the challenge of validity has not been officially made.
This does not discount the Lutheran faith in the Eucharist, but reveals your founding father Martin Luther who was a Catholic remained in “quarrel with his neighbor”.
Thus we have two revealed oppositions; 1. reconciliation back into communion 2. What is a valid Eucharist approved by a successor to the apostles, a Catholic bishop.
I wouldn’t question the faith of a Lutheran Eucharist, those who follow Martin Luther, but there are some who teach the Eucharist as a symbol and not a true presence from protestantism.
Just a lay perspective seeking full communion with our separated brethren, as time goes on I see this gap close to disappearing as our communities learn more of our histories, and it is us the living that can make this happen. The hard knock truth is, the Catholic Church is Rock and does not move, although hope can be sought through reconciliation and a Lutheran apostolate consisting of Lutheran clergy, instead of a Lutheran independent Church apart from the Catholic bishop.
Peace be with you
I’m sorry if my reasoning is askew, here, but I have to get this question out.
Why is Lutheran Eucharist considered to be invalid in the Catholic Church, when the sacraments are mediated not by man, but by Christ? By God? The Sacraments in any church should be considered perfectly valid, regardless of the state of the minister (Holy Orders).