What was Swami Vivekananda's view on animal sacrifices? Did he support it or criticise it?
First let us discuss Swamiji's views on vegeterianism:
The taking of life is undoubtedly sinful; but so long as vegetable food is not made suitable to the human system through progress in chemistry, there is no other alternative but meat-eating. So long as man shall have to live a Râjasika (active) life under circumstances like the present, there is no other way except through meat-eating. It is true that the Emperor Asoka saved the lives of millions of animals by the threat of the sword; but is not the slavery of a thousand years more dreadful than that? Taking the life of a few goats as against the inability to protect the honour of one's own wife and daughter, and to save the morsels for one's children from robbing hands — which of these is more sinful? Rather let those belonging to the upper ten, who do not earn their livelihood by manual labour, not take meat; but the forcing of vegetarianism upon those who have to earn their bread by labouring day and night is one of the causes of the loss of our national freedom. Japan is an example of what good and nourishing food can do.
We must remember that advocating meat-eating was equivalent to accepting animal-sacrifice,, as 'vritha-mansa' (non-offered meat) was not much accepted at that time in society.
And He, being born in a Shakta family, accepted animal sacrifice wholeheartedly. During the first Durga Puja at Belurmath in 1901, Swamiji asked His disciple Sarat Chandra Chakrabarti to bring one copy of Ragunandan's book on Durga-Puja. After reading the book, Swamiji says to Saratchandra:
If possible, we shall perform the worship of the Divine Mother this year. Raghunandan says: navamyaam pujayet devim krittva rudhira-kardamam (on Navamai tithi,Devi should be worshipped by creating a mud of animal blood). If the Divine Mother wishes, we will also do that.(Swami-Sishya-Samvad, Saratchandra Chakravarti,Udbodhan, page 229).
But the sacrifice did not take place because of Sri Sarada Devi's objection.
He also told Nivedita : If one drop of blood is required to complete the picture (ie for fulfilling the requirement of worship), what's the harm? ( Reference: Nivedita Lokamata, Sankariprasad Basu).