It is a solemn thing to say that the rider on the first, white, horse in Revelation 6:2 is the anti-Christ, for if it turns out to be Christ on that white horse, then blasphemy will have been uttered. The question here simply says, "The first horseman is interpreted by some to be the AntiChrist".
As that sentence is fundamental to exploring the understanding, and whether another text, 2 Thessalonians 2:6-7, supports the OP wondering if the breaking open of the first seal permits the anti-Christ to ride forth on that first, white horse, the Revelation text requires examination. To do that, let it first be pointed out that Revelation chapters 4 to 6 mark the second section of the entire book. (There are 7 sections in total.) Those chapters begin to open up how the risen Christ alone is able to break the 7 seals of the book in the hand of the Almighty, leading to his glorious return as heir of the world, occupying the throne of world dominion that The anti-Christ is trying to usurp. Now follows quotes from a 600+ page exposition of the book of Revelation, dealing with the opening of that first seal:
"The book of God's rights on his terms to all Creation remains to
mankind as if it were permanently sealed... When the Lamb took the
book from the right hand of him that sat upon the throne there was an
immediate and overwhelming response not only from the redeemed but
from the Creation itself. For the issue is the Creation. The book
relates to the sole rights of the Creator to the inheritance of the
earth, despite the kingdoms of this world in contest for the throne of
world dominion.
And, in sequence, a horse and rider appear. These are the four
horsemen of the Apocalypse, unique to the first four seals. Here is a
going forth from heaven to the earth of that which is of God. And to
what end? To reveal to a blind, fallen and rebellious world, and its
rulers and nations, that 'The earth is the Lord's and the fulness
thereof'. Moreover, that what the world regards as the 'normality' of
its divorce from the throne in the heavens, and from him that sits
upon it, is intolerable to the Almighty. He will establish his
Anointed upon the throne of world dominion to inherit the earth, and
the mysterious horsemen begin to show how he will do so... [Then
Zechariah's vision in 520 B.C. is examined, re. horses and four
chariots he saw, signifying divine powers, then back to Revelation
6:1-2]
The first horse was white. White is indicative of purity: Matthew
17:2, Luke 9:29, 'his raiment was white and glistening.' That is
pure white. Cleanliness and purity are combined in the vision of the Ancient of days, Daniel 7:9... White is also indicative of
righteousness. The Lamb's wife, Revelation 19:8, was granted to be
arrayed in fine linen, clean and white: 'for the fine linen is the
righteousness of saints.' Once ,ore, righteousness is combined with
judgment, Revelation 15:6 'The seven angels came out of the temple,
having the seven plagues. clothed in pure and white linen.'
So that a white horse would convey concepts judgment, righteousness,
cleanliness, and purity. 'And he that sat on him had a bow; and a
crown was given unto him; and he went forth conquering and to
conquer.' But first, if the rider sat upon a horse conveying such a
character, that character must suit the rider.
If so, the rider is Christ. But Christ as fulfilling a certain office.
He has a bow. Yet no mention is made of arrows. Here is a mystery. It
is warfare but not with carnal weapons. There is an indication of the
instruments of war, but a withholding of their being used in violence.
There is no worldly application. It is war, but it is spiritual war.
A crown was given unto him. Then he must be a King. And if a King,
then of a kingdom. But, saith he, 'My kingdom is not of this world: if
my kingdom were of this world, then would my servants fight, that I
should not be delivered to the Jews: but now is y kingdom not from
hence', John 18:36. The crowned rider on the white horse depicts
Christ in his progress through time, going forward in his glorious
majesty, unseen by the world, but worshipped in the kingdom.
The rider is Christ, but Christ in this distinct office of King over
the kingdom. He is invisibly and secretly bringing in his kingdom in
such a way that the world does not even know what is happening.
Throughout time he rides gloriously, he triumphs in majesty...
There are two words for crown in Greek. One is stephanos. This is
that spoken of in Revelation 6:2... It's the same in Revelation 14:14,
'And I looked, and behold a white cloud, and upon the cloud sat like
unto the Son of man, having on his head a golden crown, and in his
hand a sharp sickle.' Here is the same rider, the King, having reached
the conclusion of his ride, and, as Son of man, ready to thrust in the
sickle and reap the harvest of the earth in the Last Judgment." The
Revelation of Jesus Christ, John Metcalfe, pp. 116, 145-6, 152-4,
1998, republished 2022,
http://www.johnmetcalfepublishingtrust.co.uk/contact_us.htm
Having explored the meaning of Revelation 6:2, comparing it with related texts, the blasphemous idea that the rider is The anti-Christ has been exposed. This means that there is no need to then see if 2 Thessalonians 2:6-7 applies. It cannot, for the rider on the white horse is Christ Jesus, setting forth to spiritually conquer but without violent force, his triumphant ride ending in Revelation 14:14 when he returns as the rightful King, in judgment.
