This answer says:
All these Puranic stories are taken from the book 'Hindu Gods and Goddesses' by Swami Harshananda. Swami Harshananda of the Ramakrishna Order is an Advaitist and does not take the Puranic stories seriously. The learned Swami gives several views regarding the meaning of the elephant head.
Also, has it got to do with the teachings of Ramakrishna or Vivekananda or the Advaita philosophy itself?
It is hard to definitively answer this question without a survey. Swami Vivekananda himself considered the question of historicity of the Puranas to be an unimportant issue. I think he preferred to read the Puranas allegorically.
Q. — Here and there attempts are made to import into the Purânas hidden ideas which are said to have been allegorically represented. Sometimes it is said that the Puranas need not contain any historical truth, but are mere representations of the highest ideals illustrated with fictitious characters. Take for instance, Vishnupurâna, Râmâyana, or Bhârata. Do they contain historical veracity or are they mere allegorical representations of metaphysical truths, or are they representations of the highest ideals for the conduct of humanity, or are they mere epic poems such as those of Homer?
A. — Some historical truth is the nucleus of every Purana. The object of the Puranas is to teach mankind the sublime truth in various forms; and even if they do not contain any historical truth, they form a great authority for us in respect of the highest truth which they inculcate. Take the Râmâyana, for illustration, and for viewing it as an authority on building character, it is not even necessary that one like Rama should have ever lived. The sublimity of the law propounded by Ramayana or Bharata does not depend upon the truth of any personality like Rama or Krishna, and one can even hold that such personages never lived, and at the same time take those writings as high authorities in respect of the grand ideas which they place before mankind. Our philosophy does not depend upon any personality for its truth. Thus Krishna did not teach anything new or original to the world, nor does Ramayana profess anything which is not contained in the Scriptures. It is to be noted that Christianity cannot stand without Christ, Mohammedanism without Mohammed, and Buddhism without Buddha, but Hinduism stands independent of any man, and for the purpose of estimating the philosophical truth contained in any Purana, we need not consider the question whether the personages treated of therein were really material men or were fictitious characters. The object of the Puranas was the education of mankind, and the sages who constructed them contrived to find some historical personages and to superimpose upon them all the best or worst qualities just as they wanted to, and laid down the rules of morals for the conduct of mankind. Is it necessary that a demon with ten heads (Dashamukha) should have actually lived as stated in the Ramayana? It is the representation of some truth which deserves to be studied, apart from the question whether Dashamukha was a real or fictitious character. You can now depict Krishna in a still more attractive manner, and the description depends upon the sublimity of your ideal, but there stands the grand philosophy contained in the Puranas.
The Complete Works of Swami Vivekananda, Volume 5, Interviews, With the Swami Vivekananda at Madura (The Hindu, Madras, February, 1897)
You have said that Swami Harshananda does not take puranic stories seriously. This is your opinion, he doesn't say that. You are projecting your own opinion. There is no 'dogma' as to whether any specific or all puranic stories are taken as truth; rather it is up to the individual. Do the followers of Siva accept the Vishnu Purana stories as true? Do the followers of Vishnu accept the Siva Purana stories as true? 'Belief' as to the historical accuracy of anything does not lead to liberation. It matters little what you as an individual believe. What matters is to love God, to think of God, and realize God. Realize God, then you can ask Him directly what stories are true.
Swami Vivekananda says (Complete Works Vol 1 - https://advaitaashrama.org/):
The aim is to get rid of nature's control over us. That is the goal of all religions. Each soul is potentially divine. The goal is to manifest this divinity within, by controlling nature, external and internal. Do this either by work, or worship, or psychic control or philosophy--by one or more or all of these--and be free. This is the whole of religion. Doctrines, or dogmas, or rituals, or books, or temples, or forms, are but secondary details.
And Ramakrishna Parmahamsa says (Gospel of Sri Ramakrishna, Chapter 29 [Chapter 2 'The Durga Puja Festival' Vol 2 in this link] - https://www.ramakrishnavivekananda.info/gospel/gospel.htm):
"But I say that we are all calling on the same God. Jealousy and malice need not be. Some say that God is formless, and some that God has form. I say, let one man meditate on God with form if he believes in form, and let another meditate on the formless Deity if he does not believe in form. What I mean is that dogmatism is not good. It is not good to feel that my religion alone is true and other religions are false. The correct attitude is this: My religion is right, but I do not know whether other religions are right or wrong, true or false. I say this because one cannot know the true-nature of God unless one realizes Him. Kabir used to say: 'God with form is my Mother, the Formless is my Father. Which shall I blame? Which shall I praise? The two pans of the scales are equally heavy.'
"Hindus, Mussalmans, Christians, Saktas, Saivas, Vaishnavas, the Brahmajnanis of the time of the rishis, and you, the Brahmajnanis of modern times, all seek the same object. A mother prepares dishes to suit the stomachs of her children. Suppose a mother has five children and a fish is bought for the family. She doesn't cook pilau or kalia for all of them. All have not the same power of digestion; so she prepares a simple stew for some. But she loves all her children equally.
"Do you know my attitude? I love all the preparations of fish. I have a womanly nature. (All laugh.) I feel myself at home with every dish — fried fish, fish cooked with turmeric powder, pickled fish. And further, I equally relish rich preparations like fish-head, kalia, and pilau. (All laugh.)
"Do you know what the truth is? God has made different religions to suit different aspirants, times, and countries. All doctrines are only so many paths; but a path is by no means God Himself. Indeed, one can reach God if one follows any of the paths with whole-hearted devotion. Suppose there are errors in the religion that one has accepted; if one is sincere and earnest, then God Himself will correct those errors. Suppose a man has set out with a sincere desire to visit Jagannath at Puri and by mistake has gone north instead of south; then certainly someone meeting him on the way will tell him: 'My good fellow, don't go that way. Go to the south.' And the man will reach Jagannath sooner or later.
"If there are errors in other religions, that is none of our business. God, to whom the world belongs, takes care of that. Our duty is somehow to visit Jagannath. (To the Brahmos) The view you hold is good indeed. You describe God as formless. That is fine. One may eat a cake with icing, either straight or sidewise. It will taste sweet either way.
"But dogmatism is not good. You have no doubt heard the story of the chameleon. A man entered a wood and saw a chameleon on a tree. He reported to his friends, 'I have seen a red lizard.' He was firmly convinced that it was nothing but red. Another person, after visiting the tree, said, 'I have seen a green lizard.' He was firmly convinced that it was nothing but green. But the man who lived under the tree said: 'What both of you have said is true. But the fact is that the creature is sometimes red, sometimes green, sometimes yellow, and sometimes has no colour at all.'
"God has been described in the Vedas as both with attributes and without. You describe Him as without form only. That is one-sided. But never mind. If you know one of His aspects truly, you will be able to know His other aspects too. God Himself will tell you all about them. (Pointing to two or three Brahmo devotees) Those who come to your Samaj know both this gentleman and that."
