Do Neo-Vedantins reject the authority of the Dharma Shastras? If so, why?
Not sure what Neo-Vedanta is, but I am answering with the views of Swami Vivekananda on the subject.
In the first place, we have to understand a little about our scriptures. Two ideals of truth are in our scriptures; the one is, what we call the eternal, and the other is not so authoritative, yet binding under particular circumstances, times, and places. The eternal relations which deal with the nature of the soul, and of God, and the relations between souls and God are embodied in what we call the Shrutis, the Vedas. The next set of truths is what we call the Smritis, as embodied in the words of Manu. Yâjnavalkya, and other writers and also in the Purânas, down to the Tantras. The second class of books and teachings is subordinate to the Shrutis, inasmuch as whenever any one of these contradicts anything in the Shrutis, the Shrutis must prevail. This is the law. The idea is that the framework of the destiny and goal of man has been all delineated in the Vedas, the details have been left to be worked out in the Smritis and Puranas. As for general directions, the Shrutis are enough; for spiritual life, nothing more can be said, nothing more can be known. All that is necessary has been known, all the advice that is necessary to lead the soul to perfection has been completed in the Shrutis; the details alone were left out, and these the Smritis have supplied from time to time.
"and the other is not so authoritative, yet binding under particular circumstances, times, and places" -- That means he accepts that the other i.e the Dharmashastras of Manu etc are authoritative in certain times, places.. although not as authoritative as the Vedas.. So he does not completely reject the Smriti's authority.
Furthermore, he says:
The second class of books and teachings is subordinate to the Shrutis, inasmuch as whenever any one of these contradicts anything in the Shrutis, the Shrutis must prevail. This is the law.
Now, this rule or law itself (that if Sruti contradicts a Smriti the later should be rejected) is not from the Vedas but found in the Smritis and Puranas. So, he is accepting the authority of Smritis and Puranas in this case too.
I dont like the term Neo-Vedanta. But this is what Swami Vivekananda wrote in His introduction to Rajyoga:
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.
I feel this is the essence of true spirituality. This gives ME the essence of the Vedanta, the essence of Dharma and the essence and importance of the Dharma Shastras.
Swami Vivekananda's opinion in a letter written on 30 May 1887---just one year after His Guru's passing away also makes the role of the Dharma -sastras clear to ME:
The Smritis and the Puranas are productions of men of limited intelligence and are full of fallacies, errors, the feelings of class and malice. Only parts of them breathing broadness of spirit and love are acceptable, the rest are to be rejected. The Upanishads and the Gita are the true scriptures; Rama, Krishna, Buddha, Chaitanya, Nanak, Kabir, and so on are the true Avatâras, for they had their hearts broad as the sky — and above all, Ramakrishna.
I know of course that He was too young at that time, was very emotional and always had infinite compassion for all. So I take the last message by sprit, NOT by words.