Are mainline Protestants our Brothers in Christ by virtue of the Trinitarian Baptism? [Catholic] [duplicate]

Question

If I am not mistaken, water baptism is one of the 7 sacraments and it can be performed by laymen and must not necessarily involve clergy. In such a case, since Protestants have no apostolic succession unlike the Orthodox, are their baptisms valid in their own right?

To be clear, belief in the Holy Trinity is a prerequisit that seems obvious and mainline Protestants do believe in the Holy Trinity. Some of the Reformers had a similar view of Catholics being their brothers by baptism, notably John Calvin.

EDIT : My question is different to certain others because it deals with the validity of the sacrement of baptism in Protestant circles instead of merely if God will have extraordinary mercy on Protestants as opposed to ordinary mercy with sacrements. If the mercy is extraordinary it almost pushes salvation in Protestantism to the level of salvation in for instance paganism, where there are no elements of the Church to draw life from like a source of water. However if Protestantism has ordinary significance then we can safely say that Protestants are Christians, and not simply hope that they are.

Answer 1

The answer is yes, the Catholic Church views Protestants as brothers by virtue of the baptismal formula of Father, Son, Spirit.

Wounds to unity

817 In fact, "in this one and only Church of God from its very beginnings there arose certain rifts, which the Apostle strongly censures as damnable. But in subsequent centuries much more serious dissensions appeared and large communities became separated from full communion with the Catholic Church - for which, often enough, men of both sides were to blame." The ruptures that wound the unity of Christ's Body - here we must distinguish heresy, apostasy, and schism - do not occur without human sin:

Where there are sins, there are also divisions, schisms, heresies, and disputes. Where there is virtue, however, there also are harmony and unity, from which arise the one heart and one soul of all believers.

818 "However, one cannot charge with the sin of the separation those who at present are born into these communities [that resulted from such separation] and in them are brought up in the faith of Christ, and the Catholic Church accepts them with respect and affection as brothers . . . . All who have been justified by faith in Baptism are incorporated into Christ; they therefore have a right to be called Christians, and with good reason are accepted as brothers in the Lord by the children of the Catholic Church."

PS. There are those of the Catholic Church who disagree with the Catholic Church called sedevancatists.

Answer 2

According to the official Catholic theology from Vatican II, the answer is YES. Here's a quote, I've cited before on a similar topic.

Wikipedia Quote)

J. M. R. Tillard goes into detail, in New Catholic Encyclopedia, about "the development of a carefully nuanced vocabulary, consistent with Vatican II Ecclesiology," which evolved from "the idea of membership in favor of that of incorporation" and has its categorization found in the dogmatic constitution Lumen gentium (LG) which Tillard describes: Catholics are defined as "'being incorporated' (incorporatio), qualifying the term with the adverb 'fully' (plene) and emphasizing that full incorporation requires the presence of the Holy Spirit."[b] Non-Catholics and catechumens are defined as "'being linked' (conjunctio) to the Church, again carefully stressing the role of the Holy Spirit in each case."[c] Non-Christians are defined as "'being related' (ordinantur), a term that suggests a dynamic relationship, an orientation toward the Church."[d] "Every shade of difference in meaning among these terms is important," emphasizes Tillard. "But the terms acquire their full force only in the light of the most authoritative commentaries on them," UR and Nostra aetate (NA). "Then, supposing the nuances indicated, the richness of such expressions as the following becomes clear: 'Churches and ecclesial communities';[e] 'separated brethren';[f] 'separated Churches and ecclesial communities';[g] 'full communion'—'imperfect communion'."[10][h] "But thanks to its ecclesiology," wrote Tillard, "Vatican II was able to affirm at the same time that Churches or ecclesial communities separated from the Catholic Church are part of the single Church, and that nevertheless incorporation in Christ and His Church possesses within the Catholic Church the fullness that it does not have elsewhere."

Unitatis redintegratio (Wikipedia)

Answer 3

Certainly not.

If a protestant is culpable of his exclusion from the Catholic Church. Yes the sacrament is valid, but by culpably rejecting dogma, he can possibly bring upon himself excommunication and therefore rejects the salvation offered to him.

Excommunication does not mean damnation, but if culpably persisted it will lead to damnation.

I highlighted culpability, to emphasise only God knows the full culpability of a man's sin!

An example of the beliefs that can lead someone to excommunication are...

If any one saith, that, since Adam's sin, the free will of man is lost and extinguished; or, that it is a thing with only a name, yea a name without a reality, a figment, in fine, introduced into the Church by Satan; let him be anathema.

Council of Trent Session 6 Canon 5

If any one saith, that by faith alone the impious is justified; in such wise as to mean, that nothing else is required to co-operate in order to the obtaining the grace of Justification, and that it is not in any way necessary, that he be prepared and disposed by the movement of his own will; let him be anathema.

Council of Trent Session 6 Canon 9

If any one saith, that it is necessary for every one, for the obtaining the remission of sins, that he believe for certain, and without any wavering arising from his own infirmity and disposition, that his sins are forgiven him; let him be anathema.

Council of Trent Session 6 Canon 13

If any one saith, that baptism is free, that is, not necessary unto salvation; let him be anathema.

Council of Trent Session 7 Canon 5 on Baptism

If any one denieth, that, in the sacrament of the most holy Eucharist, are contained truly, really, and substantially, the body and blood together with the soul and divinity of our Lord Jesus Christ, and consequently the whole Christ; but saith that He is only therein as in a sign, or in figure, or virtue; let him be anathema.

Council of Trent Session 13 Canon 1

A few groups could be found guilty for at least one of these.

Answer 4

Although they might be validly baptized (anyone can baptize), they are not members of the Church because they do not believe the Catholic faith in its entirely.

As Pope Pius XII wrote in his encyclical Mystici Corporis Christi:

Actually only those are to be included as members of the Church who have

1. been baptized

and

2. profess the true faith,*

and

3. who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed.

“For in one spirit” says the Apostle, “were we all baptized into one Body, whether Jews or Gentiles, whether bond or free.” As therefore in the true Christian community there is only one Body, one Spirit, one Lord, and one Baptism, so there can be only one faith. And therefore if a man refuse to hear the Church let him be considered — so the Lord commands — as a heathen and a publican. It follows that those [who] are divided in faith or government [e.g., the Protestants] cannot be living in the unity of such a Body, nor can they be living the life of its one Divine Spirit.

^{*in its entirely; cf. Satis Cognitum}

Protestants are at least material heretics; they do not hold the same faith as Catholics. They deny the papacy, a truth necessary for being a member of the Church. They do not even recognize the visible Church (its government). And, as Pope Leo XIII said in Satis Cognitum, an encyclical on the unity of the Church consisting in being “one in faith, in government, and in communion:”

The practice of the Church has always been the same, as is shown by the unanimous teaching of the Fathers, who were wont to hold as outside Catholic communion, and alien to the Church, whoever would recede in the least degree from any point of doctrine proposed by her authoritative Magisterium.

^{adapted from this answer; cf. also this answer}