In classical Advaita Vedanta, the idea is a traditionally pious person need not be spiritual. But if that person wants to become spiritual, conventional religiosity is a good preparation. Can you become a non-dualist without all that God stuff? Yes, you can. However, that was not the attitude of the traditional AdvaitA Vedanta.
Swami Sarvapriyananda teaches the Mundaka Upanishad which one of the major Upanishads belonging to the Atharva Veda. Mundaka means ''shaved'' like a shaved head. The teachings revealed in this Upanishad are meant to leave the student clean, or shaved of the veil of ignorance. Indeed, the study of this Upanishad has been traditionally confined to the shaven-heads, or the sannyasins, who have renounced everything and devoted themselves exclusively to contemplation. The book consists of 64 Mantras (verses) split across Mundakas (parts) and Khandas (sections) as follows:
Mundaka 1 - Khanda 1 - 9 mantras (1.1.1 - 1.1.9)
Mundaka 1 - Khanda 2 - 13 mantras (1.2.1 - 1.2.13)
Mundaka 2 - Khanda 1 - 10 mantras (2.1.1 - 2.1.10)
Mundaka 2 - Khanda 2 - 11 mantras (2.2.1 - 2.2.11)
Mundaka 3 - Khanda 1 - 10 mantras (3.1.1 - 3.1.10)
Mundaka 3 - Khanda 2 - 11 mantras (3.2.1 - 3.2.11)
Reference books:
1. Mundaka Upanisad translated by Swami Gambhirananda - https://www.vedanta.com/store/mundaka-upanisad-with-the-commentary-of-sankaracarya_moreinfo.html (or)
2. Eight Upanisads Vol. 2 translated by Swami Gambhirananda - https://www.vedanta.com/store/Eight-Upanishads-Commentary-by-Shankara_moreinfo.html