Most Indians don't care about this question, since their first (and in many cases, only) concern is survival.
Other Hindus take the view that the Gita should be taught. This is, actually, a sectarian Hindu position, as the Gita is not universally revered by Hindus. The scriptures that are universally revered by Hindus are the Vedas.
So, in sofar as we Hindus want a religious text to be taught in schools, we should not support the teaching of a religious book revered by one section of Hindus, we should support the teaching of the Vedas, which are revered by all Hindus.
Of course, there are secular Hindus who oppose the teaching of any and all religious scripture in our schools.
And that is the mainstream and official position in our country.
My own view is that all religious scriptures should be taught in schools, as that is the only way of creating a genuine secularism as against the superficial secularism we have at present.
Let the leaders of all religions be invited to send their authorised teachers to our schools. And, in order to ensure freedom of choice, let all students freely choose in which THREE religious texts they wish to receive instruction.
Of course, we should ensure that it is the texts themselves that are being examined - as the time should not be wasted on hearing merely the views of any religious teacher.
As students nowadays do not have unlimited time, I would suggest that what is at present the time given to Moral Instruction should continue, but that, within that time, provisio is made for at least one alternative lesson each year from each of the six major traditions (Hindu, Muslim, Christian, Buddhist, Jain and Sikh - not in any particular order but simply the order in which they spring to my mind at this moment)