Is Shalagram worship forbidden to non-Brahmins?
No. It is not forbidden.
The importance of Gandaki river is explained in chapter 20 of Patala Khanda of Padma Purana. In that chapter, the importance of śālagrāma is also said.
The disc born (i.e. found) in Dvaravati and the stone born (i.e. found) in Gandaki, destroy in a moment men's sins earned during a hundred existences. Even if a man would have committed a thousand sins, he would be purified by drinking the water of (i.e. flowing from) a śālagrāma.
ब्राह्मणः क्षत्रियो वैश्यः शूद्रो वेदपतिस्तथा ।
शालग्रामं पूजयित्वा गृहस्थो मोक्षमाप्नुयात् ॥
A brahmana, ksatriya, vaiśya or śudra householder, who is on the path of the Vedas (i.e. behaves according to the Vedic injunctions), would obtain salvation on worshipping a śālagrāma.
However, the worship of śālagrāma is mostly done by those who have a tradition of worship among them. We should be of good conduct and very pious while worshipping a śālagrāma because it is considered form of Lord Viṣṇu.
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