All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu`alayhi wa sallam, is His Slave and Messenger.
The difference between the second and third opinions is that the second opinion holds that his repentance is not accepted as to the worldly rulings - meaning that he is to be treated as a disbeliever: he is not washed, shrouded, prayed over, or buried alongside Muslims. However, this view is weak, as Ibn ʿUthaymīn 
  himself stated in the very source from which you have quoted him:
“But this opinion is weak, because the correct view is that repentance is accepted whenever it is made properly. Yet, if the person had insulted Allah (before repentance), he is not to be executed; but if he had insulted the Messenger, then he is to be executed.” [End quote]
As for the Hereafter, his repentance is valid according to all three opinions - if it is sincere, Allah will accept it from him - due to the generality of the texts affirming that repentance is accepted from all sins. Among them is the saying of Allah, the Exalted:
{Say: O My servants who have transgressed against themselves, do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Truly, He is the Most Forgiving, the Most Merciful.} [Quran 39:53]
As for the third opinion, its meaning is that his repentance is accepted, and he will be considered as a Muslim if he is sincere in his repentance. Thus, the rulings of Muslims apply to him in both this world and the Hereafter. However, he is still to be executed as a legal punishment, because the right of the Prophet, sallallaahu 'alayhi wa sallam, after his death cannot be pardoned by anyone. Ibn Taymiyyah 
   said in As-Ṣārim al-Maslūl:
“Insulting the Prophet, sallallaahu 'alayhi wa sallam, is an insult to one who has died, and such an offence is never dropped by repentance.” [End quote]
Accordingly, this is our response concerning the classification mentioned in the question. However, the issue has more detailed discussion which can be found in As-Ṣārim al-Maslūl by Ibn Taymiyyah 
.
Allah knows best.