Orcs don't need to do the kinship quest.
An orc vampire I would imagine would be treated by orcs the same a nord vampire would be treated by nords... hostile.
But I have never played a skyrim vampire so I can't really answer that I guess.
You are not considered to be of the OrcRace while you are a vampire, so you will need to acquire Blood-Kin status some other way, if you don't have it already.
This has been fixed by the Unofficial Patch.
What's happening is that, when you approach, the game looks at a Race keyword (specifically, it's looking for the 'OrcRace' keyword). The problem is that the game is very literal, so it's looking for that specific keyword. Once an Orc becomes a Vampire, their race changes to 'OrcVampireRace'. Now, you and I can look at that and say, 'That's an Orc'. The game, however, is looking for the specific keyword 'OrcRace', and an Orc Vampire loses that keyword, so the game thinks you're not an Orc. It therefore directs you to find the Forgemaster's Fingers, as any other race would have to. The Unofficial Patch adds the 'OrcVampireRace' to the list of keywords that the game is looking for, so you can get in without doing the quest. However, the Unofficial Patch requires you to be playing on the PC, and to actually download the patch, so it's not available for everyone.
As for the response, I'd imagine it's just like Resident said: if you're a Stage 4 Vampire, you're going to have a bad time.