From a traditional Christian reading of Scripture, yes. Jesus repeatedly connects faith in Himself with eternal life and unbelief with condemnation.
For example, He asks, "He that believeth on him is not condemned: but he that believeth not is condemned already" (John 3:18), and "He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life" (John 3:36).
At the same time, I'd ask a question Jesus often would have pressed: Who is Jesus?
If He is truly who He claimed to be, then unbelief in Him is not merely rejecting a doctrine, but rejecting the very source of life God has provided.
So the discussion isn't really about whether Christians think Hindus, Muslims, atheists, or anyone else are "bad enough" for judgment. The real issue is whether Christ is the unique Savior.
If He is, then our response to Him necessarily has eternal significance.
If He is not, then Christianity itself would be false. That's the underlying question.