Isn't that what they used to say about other races? Or women?
Not really. It was always understood (for example) that women knew they were looking at an image of themselves in the mirror, could manage the (quite complex) analysis of consciousness necessary to master lying and had the same ability to use concepts in language.
A very, very small number of animal species get all that. If you're discussing (say) a bird that insistently assaults a mirror, apparently because there's an aggressive bird in there that looks just like it, then asking whether that bird wonders if there is an afterlife is bizarre - we've got no handle on what being that bird feels like at all, but there is absolutely no observable reason to suppose it worries about anything other than its surroundings.
There are some things that seem to be in a different league: big primates, cetaceans, elephants. It appears to be extremely species-specific. I'd still be extremely wary of imagining that we could "relate" in any meaningful sense to a dolphin though.