Is a marriage solemnised only through religious rituals, without registration, still legally valid?

Generally, yes — a marriage validly solemnised according to the customs and rituals recognised under your applicable personal law is legally valid even without separate registration, since registration is largely meant to create official documentary proof of a marriage that has already validly taken place, rather than being what actually creates the marriage itself.

That said, not registering your marriage can create practical difficulties — for matters like passport applications, visa processes, or various other transactions requiring documentary marriage proof, having a registration certificate makes life considerably easier than relying solely on witnesses or ritual proof if the validity of your marriage is ever questioned.

Several states have also moved toward making registration compulsory, with penalties for non-compliance, even though non-registration doesn't typically void an otherwise validly solemnised marriage. Given the practical advantages, it's generally advisable to get your marriage registered even after the fact if you haven't already, which is usually a fairly straightforward administrative process.