Vivekananda advocated a return to a karma-guna based varna system and not the last name based jati system. Both the karma-guna based varna system and the last name based jati system are birth based. The present varna of a person is dependent on the past karma and guna in the karma-guna based varna system and a person can indeed transcend his varna through spiritual practice. The jati or caste of a person is decided by the last name of a person's family in the last name dependent caste system and it is impossible to change one's caste.
I fully agree with the educated classes in India that a thorough
overhauling of society is necessary. But how to do it? The destructive
plans of reformers have failed. My plan is this. We have not done
badly in the past, certainly not. Our society is not bad but good,
only I want it to be better still. Not from error to truth, nor from
bad to good, but from truth to higher truth, from good to better,
best. I tell my countrymen that so far they have done well — now is
the time to do better.
Now, take the case of caste — in Sanskrit, Jâti, i.e. species. Now,
this is the first idea of creation. Variation (Vichitratâ), that is to
say Jati, means creation. "I am One, I become many" (various Vedas).
Unity is before creation, diversity is creation. Now if this diversity
stops, creation will be destroyed. So long as any species is vigorous
and active, it must throw out varieties. When it ceases or is stopped
from breeding varieties, it dies. Now the original idea of Jati [i.e.
Varna] was this freedom of the individual to express his nature, his
Prakriti, his Jati, his caste; and so it remained for
thousands of years. Not even in the latest books is inter-dining
prohibited; nor in any of the older books is inter-marriage forbidden.
Then what was the cause of India's downfall? — the giving up of this
idea of caste. As Gitâ says, with the extinction of caste
the world will be destroyed. Now does it seem true that with
the stoppage of these variations the world will be destroyed? The
present caste is not the real Jati, but a hindrance to its
progress. It really has prevented the free action of Jati, i.e. caste
or variation. Any crystallized custom or privilege or
hereditary class in any shape really prevents caste
from having its full sway; and whenever any nation ceases to produce
this immense variety, it must die. Therefore what I have to tell you,
my countrymen, is this, that India fell because you prevented and
abolished caste [Varna]. Every frozen aristocracy or privileged class
is a blow to caste and is not-caste. Let Jati
have its sway; break down every barrier in the way of caste,
and we shall rise. Now look at Europe. When it succeeded in giving
free scope to caste and took away most of the barriers that
stood in the way of individuals, each developing his caste —
Europe rose. In America, there is the best scope for caste
to develop, and so the people are great. Every Hindu knows
that astrologers try to fix the caste of every boy or girl as
soon as he or she is born. That is the real caste — the individuality,
and Jyotisha (astrology) recognises that. And we can only rise by
giving it full sway again. This variety does not mean inequality, nor
any special privilege.
This is my method — to show the Hindus that they have to give up
nothing, but only to move on in the line laid down by the sages and
shake off their inertia, the result of centuries of servitude. Of
course, we had to stop advancing during the Mohammedan tyranny, for
then it was not a question of progress but of life and death. Now that
that pressure has gone, we must move forward, not on the lines of
destruction directed by renegades and missionaries, but along our own
line, our own road. Everything is hideous because the building is
unfinished. We had to stop building during centuries of oppression.
Now finish the building and everything will look beautiful in its own
place. This is all my plan. I am thoroughly convinced of this. Each
nation has a main current in life; in India it is religion. Make it
strong and the waters on either side must move along with it. This is
one phase of my line of thought. In time, I hope to bring them all
out, but at present I find I have a mission in this country also.
Moreover, I expect help in this country and from here alone. But up to
date I could not do anything except spreading my ideas. Now I want
that a similar attempt be made in India.
The Complete Works of Swami Vivekananda, Volume 4, Writings Prose, A Plan of Work for India
Vivekananda on Purusha Sukta
The doctrine of caste in the Purusha-Sukta of the Vedas does not make
it hereditary..
The Complete Works of Swami Vivekananda, Volume 6, Epistles, Second Series, VIII.
Vivekananda's opinion about Smritis on the caste issue is given in a 30th May, 1897 letter to Sri. Pramada Das Mitra.
The Smritis and the Puranas are productions of men of limited
intelligence and are full of fallacies, errors, the feelings of class
and malice. Only parts of them breathing broadness of spirit and love
are acceptable, the rest are to be rejected. The Upanishads and the
Gita are the true scriptures.
The Complete Works of Swami Vivekananda/Volume 6/Epistles - Second Series/CXXIV
Vivekananda thinks that the Rg Vedic text is talking about variation in human nature as can be seen from the letter to the Justice.