Ramakrishna was a great Sage. So which school of thought did he belong or followed.
The great mystic & Saint, Sri Ramakrishnan Paramahamsa, born in Bengal, started his journey with unflinching devotion to Maa KAli which later also took him towards the Advaita School of Vedanta, after the incident - " when he cut Maa Kali into two pieces using the sword of jnana (knowledge) ".
His Wikipedia Page quotes as follows
Sri Ramakrishna experienced spiritual ecstasies from a young age, and was influenced by several religious traditions, including devotion toward the Goddess Kali, Tantra, Bhakti and Advaita Vedanta.
Vivekananda portrayed Ramakrishna as an Advaita Vedantin.
The message of Sri Ramakrishna to the modern world, which he gave through his life and through his recorded conversations, may be briefly stated as follows:
The goal of human life is the realization of the Ultimate Reality which alone can give man supreme fulfilment and everlasting peace. This is the essence of all religions.
The Ultimate Reality is one; but it is personal as well as impersonal, and is indicated by different names (such as God, Ishvar, etc) in different religions.
Further, in his Book - "Ramakrishna Paramahamsa: Sadhaka of Dakshineswar" ,
Amiya P Sen observes:
It is difficult to be precise or categorical while placing Sri Paramahamsa within the complex range of Vedantic thoughts. There is good reason to believe that he was dissatisfied with the advaitic tendency to collapse the distinction between God and man. To illustrate this, he would employ a metaphor attributed to the Sakta-Tantric poet, Ramoprasad Sen. It is said that Ramoprasad was keen to taste the sweetness of sugar, without turning into sugar; that is, he preferred to remain in a state of dualistic bhakti rather than be drawn into a state of abstraction without identity. Sri Ramakrishnan's ecstatic attachment to the goddess KAli, his recurrent and potent use of devotional songs, his visions of various gods and goddesses, when in saadhnaa, all point to the nature of a bhakta (devotee).
On the other hand, after being initiated into sanayaasa, by a monk of Sankarite Dasanami order, he also chose to stay in a non-dualist bhava (mood) for a period of six months. Importantly too, his reading a text like Bhagavad Gita suggest not bhakti (devotion) but tyaga (renunciation), an attitude more easily identifiable with a practitioner of Jnan Marga (the Knowledge path).
Some people also give terms like "neo-vedantin", but I personally don't understand or comprehend it, whatever it might connotes.
To conclude , with this QnA discussion, and a brief reference from here and what we have discussed above, one may be able to arrive at some conclusion that - it's really not feasible nor tenable to limit Sri Ramakrishnan Paramahansa with any particular or specific ideology systems or School of thought. He was a great Hindu saint, that too, a Paramahamsa at that, whose teachings, may be accommodated and understood as jewels of universal prajna (wisdom) of truth and reconciliation with the Universal Reality we call Brahman.
Both Ramakrishna and Vivekananda were Smartic advaitists with Kali as and other deities as Ishta devatas.
seems to make convincing case that he was born a Smarta. The highly knowledgable poster Partha/Pratimaputra states
Its therefore clear that Sri Ramakrishna's family members were smarta brahmins. They had special love and devotion for Sri Ramachandra no doubt, as so many of His family members were named after Sri Ramachandra.Sri Ramachandra was their Kuladevata. But they respected all forms of Hindu deities.Rama worshipper smarta brahmins are rare in Bengal.
Sri Totaluri, the sannyasa-guru of Sri Ramakrishna,was from Dera Baba Rajpuri of Baba Ladana near Kaithal, Hariyana.He was a disciple of Sri Jnanapuri, the fifth mohant of the dera. Tota became the sixth mohant.
So Ramakrishna was properly initiated into an advaitic order of Sanyasis.
Eminent Smartists Ramakrishna would line up with
Gaudapada Govinda Bhagavatpada Adi Shankara Sureshwaracharya Padmapadacharya Hastamalakacharya Totakacharya Vachaspati Mishra Sri Ramakrishna Swami Vivekananda Sri Ramana Maharshi Sarvepalli Radhakrishnan Madhusudana Saraswati
his advaitism is crystal clear from this quote:
SRIMAT SWAMI RAMAKRISHNA AS QUOTED BY SRIMAT SWAMI CHIDBHAVANANDA: Do you know what is meant by Brahman with divine attributes? It is like a vast expanse of water with waves, ripples, billows, bubbles, sprays, froth and so on. Forms appearing in Cit-akasa or the Expanse of Consciousness can be experienced. Even the Incarnations of God come within this category.
He followed all schools Vedanta thus unifying all aspects of Hinduism. He even followed other religions even became a muslim and christian . If one goes through authentic biographies of Ramakrishna such as Ramakrishna Kathamrita and Ramakrishna Leelaprasanga, one can come to conclusion of the message of unity of Hinduism and other religions as revealed by Ramakrishna's various sadhnas(which are not limited to Hinduism).
Sri Ramakrishna has hinted that there is some truth in all schools. He did not belong to any but accepted the truth of all while not accepting the faults of all these sects.
"Listen to a story. Once a man entered a wood and saw a small animal on a tree. He came back and told another man that he had seen a creature of a beautiful red color on a certain tree. The second man replied: 'When I went into the wood, I also saw that animal. But why do you call it red? It is green.' Another man who was present contradicted them both and insisted that it was yellow. Presently others arrived and contended that it was grey, violet, blue and so forth and so on. At last they started quarrelling among themselves. To settle the dispute they all went to the tree. They saw a man sitting under it. On being asked, he replied, 'Yes, I live under this tree and I know the animal very well. All your descriptions are true. Sometimes it appears red, sometimes yellow, and at other times blue, violet, grey, and so forth. It is a chameleon. And sometimes it has no color at all. Now it has a color and now it has none. 'In like manner, one who constantly thinks of God can know His real nature; he alone knows that God reveals Himself to seekers in various forms and aspects. God has attributes; then again He has none. Only the man who lives under the tree knows that the chameleon can appear in various colors, and he knows, further, that the animal at times has no colors at all. It is the others who suffer from the agony of futile arguments........ God reveals Himself in the form which His devotee loves most."
The Gospel of Sri Ramakrishna, The Master with the Brahmo Devotees (I)