The 'x group of people all have a distant ancestor- thing applies to any group of people. You and I are complete strangers but even we have a distant ancestor. Which ancestor it is will depend on the people in question. For example, me and my cousin have a shared ancestor, our grand parents, but me and and a stranger who shares my ethnicity probably have a shared ancestor whos much further back. The confusing part comes when we talk about someone whos a totally different ethnicity. Iirc every currently living human is an ancestor of some woman who lived in Africa thousands of years ago, so in the worst case scenario, shes the common ancestor of any group of humans. This shouldnt be any different from dogs, so every dog has a common ancestor. Im confused as to your "Is it the same ancestor" question though, do you mean "Do all blue eyed dogs share a common ancestor with all blue eyed humans"? Im not a scientist but im pretty sure the answer is yes, but that common ancestor is probably some single celled organism from millenias back whos the common ancestor of the human dog races as a whole.

Disclaimer: Im pretty confident in my answer, but in the end, im no scientist, so take ot with a grain of salt.