What is the position of Catholic theology on human rights in transhumanism? What is the opinion of Catholic theology on transhumanism, especially on the possibility to create autonomous artificial intelligence that would be granted the same or similar rights as humans?
Whether Artificial Beings should be given Rights

Objection 1 A cloned human being, would be a copy of a human being and therefore have all the faculties of that previous human being.  Whether it be the same soul or a new soul is impossible to tell.  But it must be an immortal soul since an immortal soul is innate to mankind.  An artificial being could potentially be as lifelike and organic as a cloned being ad therefore imbued with an immortal soul; one would never know. 

Objection 2 Members of the animal kingdom are given rights (according to their rarity) and privileges (according to their usefulness). Even the Bible command people not mess up birds nests (Dt 22:4, 6) or make your animals work on the Sabbath (Ex 23:12).  God affords these rights and privileges to animals and he gives us dominion over them. 


  Then God said: Let us make human beings in our image, after our likeness. Let them have dominion over the fish of the sea, the birds of the air, the tame animals, all the wild animals, and all the creatures that crawl on the earth. 
  
  Genesis 1:26 - NABRE


Therefore we could give whatever rights and privileges we want to our creations.

Objection 3 If a machine was said to be "self-aware" then that machine would be said to have an interior life.  An interior life is the thing that separates man from all other creatures.  E.F. Schumacher in Guide for the Perplexed says that the difference between man's order of being and the animals is that self-awareness that thinks about others thinking.  All it would take would be a group of robots starting a book club to make us all believe they have souls. 

On the contrary, machines, no matter how carefully designed, can never have an immortal soul.

I answer that their primacy in the order of creation is below that of man (and beast). Therefore it is not fitting for them to be granted the rights in the same domain as man.  Where this Natural Law is contradicted by Human Law, the human law is unjust.  Therefore granting rights equivalent to humans to creatures without immortal souls is gravely immoral. 

Reply to Objection 1  It is wrong to put God to the test (lk 4:12).  There is no guarantee that any artificial effort on man's behalf will force God's hand in crafting an immortal soul for man's creation.  Whether or not God gives the clones individual an immortal soul is up to God and not to man. see Judie Brown's response to a question on IVF.  But we can guarantee that God will not re-order creation around creations because "The earth is the LORD's, and everything in it, the world, and all who live in it;" (Ps 24:1). 

Reply to Objection 2  Man is to be a good steward of creation because it is creation - not because he created it. 


  In our time, the Church does not simply state that other creatures are completely subordinated to the good of human beings, as if they have no worth in themselves and can be treated as we wish. The German bishops have taught that, where other creatures are concerned, “we can speak of the priority of being over that of being useful”. 
  
  Pope Francis - Laudatio Si - p. 69


We do not just give these rights and privileges to animals because we can use them, we give them because they exist, generally speaking, independent of our labors. Machines, however, do not exist independent of our labors and therefore we are justified in giving them the most burdensome tasks as well as making them work on Sundays (unless we don't want them to). 

Reply to Objection 3  Artificial Intelligence will always be Intelligence as judged by mankind to be of some value.   There might always be faster or slower rates of computation.  So, in a world where we granted rights to a self-aware robot we could either.


Let self-aware robots determine what to do with obsolete self-aware robots 
Deprecate self-aware robots ourselves (decommission them or send them to another galaxy)


In the first case, these machines would be judged in their own order (not that of mankind) and would be afforded rights in that domain (not that of mankind). Even the Angels hold to their own orders (Cherubim, Seraphim, etc...) and their souls, while immortal, are not for mankind to grant rights to. 

In the second case we would be the higher power and, out of compassion to the works of man (out of a sense of beauty, one would hope), give rights and privileges necessary to lower orders of creation (not that of mankind) because:


  A higher power can do many things that an inferior power cannot do to those which are subject to them.
  
  Summa Theologica p.1 q.96 a.1 reply to objection 4