In his introduction to On Hinduism, Ravi Heugle writes, “The establishment of a unified blueprint of life by science will exile the soul and the assumption of the existence of the soul will prove itself to be invalid. Thereafter, the soul will solely serve as a potent synonym for human identity.”
The merit of this opinion depends on how we define “soul.” In Sanskrit, the language of Hindu scripture, the word closest to “soul” is “atman” which means spirit, individual soul and the self or Self. The Self with a capital S implies identification with the divine spirit though ancient schools of Hindu Philosophy hold divergent views about unity between human spirit and a greater divine spirit.
Regardless, mainstream Hinduism considers our soul as our individuality, the part of us that in transmigration embodies the effects of our karma which preceded our birth and will succeed our death.
The real question is whether there is any eternity for individuals. Perhaps our ancestors and heirs represent the totality of our karma and thereby our souls. If that is all, it should be more than enough.
See On Hinduism by Irina Gajjar, “A Skeptic’s Perspective.”