I have used the tag/term myself on Who coined the term "neo-vedanta?" and not in the way you describe in your post ("demean...particular category of members, especially advaitins"), so, I don't support purging of this tag.
Besides, even if you delete the tag, users can still use 'Neo-Vedanta' in posts and comments, because, merely using the word doesn't break the CoC - it's the intent that matters. If someone uses the term and then follows it up with needless criticism of a sect because of the sect's liberal interpretation of scripture, then you can flag the post or comment as 'rude or abusive'.
Also, a quick survey of Prabuddha Bharata ('Awakened India'), the monthly journal of the Ramakrishna Order started by Swami Vivekananda, shows that it places no restriction on its contributors w.r.t the term's usage. E.g., in the January 2010 edition, different authors writing on the topic, 'Perspectives on Vedanta', have used 'Neo-Vedanta' (and 'Neo-Hinduism') in different ways. Some like Swami Atmapriyananda and Javier Ruiz Calderón have actually adopted and used it in a positive sense. So, I see no reason why this site should restrict users from using the term as a tag or in posts and comments.
Neo-Vedanta and the New World Order (Swami Atmapriyananda)
Three Principles of Neo-Vedanta
One of the latest acharyas to have interpreted and infused new life into Vedanta texts was Swami Vivekananda—who was naught but 'his Master's voice'. His interpretation of Vedanta is in effect a rejuvenation of the ancient texts, and is often called the 'Neo-Vedanta of Ramakrishna-Vivekananda'. We need to examine this phrase to find out what, if anything, is new in this 'Neo-Vedanta'. In order to do this, we need to ask: What exactly did Swami Vivekananda teach? He himself said: 'I have a message, and I will give it after my own fashion.' What was the message he gave?
Swami Vivekananda's message of Vedanta is based on the following foundational principles:
- divinity of the human being;
- unity of all existence, solidarity of the universe; and as a corollary to these
- the essential spirituality of life.
What Is New in Neo-Vedanta?
Although the term 'neo-Vedanta' has gained currency, there are not scholars wanting who question the use of the prefix 'neo-' before Vedanta. Their point of view is that 'neo-' smacks of a departure from the Vedanta tradition per se, a tradition handed down over the millennia via an army of illumined acharyas. They argue that it is perhaps better to say that Sri Ramakrishna and Swami Vivekananda reinterpreted, rejuvenated, and revitalized the eternal message of Vedanta, making it a living force in the modern world. The adoption of the prefix 'neo-' is perhaps misleading, for it would mean that Ramakrishna-Vivekananda added something new to the eternal Vedanta. The question now is: Is it true that they did? And if so, can this claim be justified?
Advaita Vedanta and Philosophy of Religion (Javier Ruiz Calderón)
From this critical religiosity, there is not only one true religion,
but many true religious traditions in the pragmatic sense that they
can lead humans to holiness. For each one, her or his own tradition
and the symbols it includes are the best; but one must not think
dogmatically that what is best for me is best for everyone. In fact,
we should not only tolerate other traditions but we should be open to
learning from them.
In this respect, Hinduism has been a pioneering tradition. Sri
Ramakrishna experienced in himself that the different ideas of the
Divine are different names for the same experience and that all
spiritual paths lead to the same goal. And Swami Vivekananda
proclaimed this message to the world, boldly stating in the 1893
World's Parliament of Religions held at Chicago that all religions are
true. I believe that this humanistic and universalist neo-Hinduism or
neo-Vedanta has become, despite the opposition of the more
conservative, orthodox, and dogmatic sections of Hinduism, the most
pluralistic, dialogic, and open religious tradition, and fortunately
this attitude is also gradually entering into other religions.
Advaita Vedanta: Its Vision and Possibilities (Swami Satyamayananda)
The religion of Vedanta in all its philosophical phases, called Hinduism, has moulded every aspect of Indian life—its spirituality, ethos, language, culture, and so on. Vedanta is not a closed philosophical system, and so great sages and saints come, verify, and push Vedanta to newer grounds. The fundamentals are sacrosanct but its approaches and applications are reinterpreted accordingly to new circumstances and expansion of secular or relative knowledge. The latest to do that is Swamiji. He saw Advaita Vedanta as
a panacea for all individual and social problems and preached it as such. There is a tendency in some scholars to call it neo-Vedanta but it is not really so. Swamiji made Vedanta practical.
Swami Vivekananda on Advaita Vedanta (Jeffery D Long)
Over the course of the last few decades, academic scholarship on Advaita Vedanta has had a tendency to affirm a sharp distinction between 'classical Advaita', essentially the Advaita taught by Acharya Shankara, and 'neo-Advaita' or 'neo-Vedanta', which is either traced to Swamiji or to the reformers of the Brahmo Samaj who influenced him in his early years. Often, this divide and the prefix 'neo' in front of 'Advaita' or 'Vedanta' is taken to imply some inauthenticity, as if the Vedanta of the modern period is not the 'real' Vedanta. The assumption is that the only 'real' Advaita Vedanta is that of Acharya Shankara.
The term 'neo-Vedanta' was coined by a Roman Catholic Indologist named Paul Hacker (1913–79). Hacker, as James Madaio states, 'influentially argued that Neo-Vedanta was a nationalistic movement dependent on the "assimilation" of Western ideals. The category "Neo-Vedanta", in that way, entered mainstream academic discourse as a pejorative term—indiscriminately used in reference to a number of different Hindu thinkers who held variant theological views—and connoting a sense of inauthenticity because "continuity with the past has been broken".'
Hacker's dichotomy between 'neo' and 'authentic' Vedanta depends on viewing Acharya Shankara's expression of Advaita Vedanta as definitive of authentic Vedanta, thus rendering all other thinkers' expressions of this philosophy inauthentic. If a scholar were to make an analogous move with regard to Hacker's own Roman Catholic tradition, it would render all Roman Catholic thought since Thomas Aquinas 'neoCatholicism.' Catholic thinkers of the modern period, like Hans Urs von Balthasar and Karl Rahner, not to mention Paul Hacker himself, would thereby become 'neo-Catholic'.