As per https://en.wikipedia.org/wiki/Neo-Vedanta#Criticism_of_neo-Hinduism_label
In the 20th century the German Indologist used the terms "Neo-Vedanta" and "Neo-Hinduism" polemically, to criticize modern Hindu thinkers,.Halbfass regards the terms "Neo-Vedanta" and "Neo-Hinduism" as "useful and legitimate as convenient labels", but has criticized Hacker for use that was "simplistic". Furthermore, he asks,
What is the significance and legitimacy of the "Neo" in expressions like "Neo-Hinduism and "Neo-Vedanta"? Could we speak of "Neo-Christianity" as well? In fact, I have used this term [...] and not all my Christian readers and reviewers were happy about the term.
Halbfass wrote that the adoption of the terms
"Neo-Hinduism" and "Neo-Vedanta" by Western scholars reflects Christian and European claims and perspectives which continue to be an irritant to Indians today. For Hacker, the "Neo" in "Neo-Hinduism" implies a lack of authenticity, an apologetic accommodation to Western ideas, and a hybridization of the tradition.Halbfass adds that "I have tried to argue that Hacker's radical critique reflects above all a typically Christian and European obsession with the concept of the individual person."
According to Rajiv Malhotra, an Indian-American writer, it was Paul Hacker who popularized the term 'neo-Hinduism' in the 1950s, "to refer to the modernization of Hinduism brought about by many Indian thinkers, the most prominent being Swami Vivekananda." In Malhotra's view, "Hacker charged that 'neo-Hindus', most notably Vivekananda, have disingenuously adopted Western ideas and expressed them using Sanskrit. Malhotra also notes that Hacker was a biased Christian apologist: What is less known about Hacker is that he was also an unabashed Christian apologist who freely used his academic standing to further the cause of his Christian agenda. He led a parallel life, passionately advocating Christianity while presenting the academic face of being neutral and objective According to David Smith, Hacker's belief was that the ethical values of 'neo-Hinduism" came from Western philosophy and Christianity, just in Hindu terms. Hacker also believed that Hinduism began in the 1870's. He saw Bankin Chattopadhyaya, Aruobindo, Gandhi, and Radhakishnan as its most famous proponents.
'Indra's Net' book(written by Rajiv malhotra) extensively refutes Neo-Vedanta and Neo-Hinduism as artificial fabrication.
book review - of Indra's Net : 'The present book(Indra's net) exposes the influential narrative that Hinduism was fabricated during British rule and became a dangerous new religion. The central thesis which I seek to topple asserts that (VVVVVIMP) Swamy Vivekananda plagiarized Western secular and christian ideas and then recast them in Sanskrit terminology to claim Indian origins for them. Besides critiquing this nexus and defending Vivekananda’s vision, this book also presents my own vision for the future of Hinduism and its place in the world. Hence the book has two purposes: to defend the unity of Hinduism as we practice it today, and to offer my own ideas about how to advance Vivekananda’s revolution to the next stage.'
Hence, using "Neo-Vedanta" terminology is nothing but a christian evangelist and western-civilization agenda to discredit the Indian Philosophers by showing that their ideas came from Western sources, whereas it was just genuinely coming from Indian sources. And the same proponents of "Neo-vedanta" , never approved of "Neo-christianity" terminology for the christian re-interpretations/re-telling of last century.
Few sample example of classical humanism thoughts:
समोऽहं सर्वभूतेषु न मे द्वेष्योऽस्ति न प्रिय: |
ये भजन्ति तु मां भक्त्या मयि ते तेषु चाप्यहम् || 29|
I envy no one, nor am I partial to anyone. I am equal to all. But whoever renders service unto Me in devotion is a friend, is in Me, and I am also a friend to him.
“ Sam samidyuvase vrishannagne visvaanyaarya aa | Ilaspade samidhyase sa no vasoonyaa bhara || “ – Rigveda: 10-191-1
Oh Almighty and Adorable God ! In the whole universe Thou dost the work of harmonizing and uniting, and most fully reveal Thyself in the world. We therefore, beseech Thee to bestow upon us in every way all the means that will enable us to live in peace and harmony.
Sangathan Sukta of Rigveda (from last sukta of Rigveda)
“ Sam gacchadhavam sam vadadhvam sam vo manaamsi jaanataam IDevaa bhaagam yathaa poorve sam jaanaanaa upaasate II “ – Rig: 10-191-2
God says :- Let all your activities be so directed as to lead you to one common goal (for which) let there be conferences held among you in a common language. Let all of your minds be one for according to acquire knowledge of the various lore’s. In short do as the enlightened before you in all ages did, performing their tasks in life in cooperation and harmony, with minds in full agreement for the acquisition of knowledge. Like the ancient seers also, Worship alone, Who, the only real object of your devotion.