These three quotes from our Holy Fathers are very important:
St. Athanasios the Great, Third Discourse on the Arians
That baptisms performed by heretics are perfectly useless and vain, that baptism in the name of the Holy Trinity is useless without the correct faith regarding the Holy Trinity.
"The Arians are in danger even in the very plenitude of
the mystery---baptism, I mean. For while perfection through baptism is given in the
name of the Father and of the Son, the Arians do not refer to a true Father owing to
their denial of the likeness of the essence emanating from Him: thus they deny even
the true Son, and conjuring up another in their imagination built out of nothing real,
they call this one the Son. So how can it be said that the baptism given by them is not
perfectly useless and vain? Though it does appear to be a baptism in pretense, yet in
reality it is of no help to faith and piety. For it is not he that says merely 'O Lord' that
gives a correct baptism, but he that utters the invocation of the name and at the same
time possesses a correct faith. On this account too, the Savior did not command the
Apostles to baptize merely and in a simple fashion, but on the contrary, told them
first to make disciples of those about to be baptized, and then to baptize in the name
of the Father, and of the Son, and of the Holy Spirit, in order that the faith might become
correct from their having been instructed disciples, and, thanks to their correct
faith the perfection of the baptism might be added. It is for this reason indeed that
many other heresies, true enough, do say only the names of the Holy Trinity , but inasmuch
as they do not believe these correctly and they have not a sound faith either,
the baptism given by the is of no benefit to them, owing to its lacking piety. So that
as a matter of fact the consequence is that anyone sprinkled by them is rather polluted
with impiety than redeemed from it. So the Arians, who share beliefs of Arius, though
they may read the words written and may pronounce the names of the Holy Trinity in
their baptism, yet they arc deluding and misleading those who receive their baptism at
their hands, since they are more impious than he other heretics."St. John Chrysostom in his sermon on the proposition "In the beginning there already was the Logos” - John 1:1
The baptism of heretics does not illumine the soul
"Let not the systems of the heretics fool you, my dear listener: for they have a baptism,
but no illumination; accordingly, they are baptized, it is true, with respect to the body,
but as respects he soul they are not illuminated."St. Leo the Great in his epistle to Nicetas
"For they who have received baptism from heretics, not having been previously baptized, are to be confirmed by imposition of hands with only the invocation of the Holy Ghost, because they have received the bare form of baptism without the power of sanctification. And this regulation, as you know, we require to be kept in all the churches, that the font once entered may not be defiled by repetition, as the Lord says, 'One Lord, one faith, one baptism.' And that washing may not be polluted by repetition, but, as we have said, only the sanctification of the Holy Ghost invoked, that what no one can receive from heretics may be obtained from catholic priests. This letter of ours, which we have sent in reply to the inquiries of the brotherhood you shall bring to the knowledge of all your brethren and fellow-bishops of the province, that our authority, now that it is given, may avail for the general observance."