Are mainline Protestants our Brothers in Christ by virtue of the Trinitarian Baptism? [Catholic] 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.
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, &quot;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.&quot; 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 &quot;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.&quot;

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