That wouldn't require any immunity, that stops anything from getting in in the first place. Herd immunity is enough immunity that even if someone does catch the virus an outbreak is impossible because the chain is statistically guaranteed to break.
My simplistic and possibly incorrect understanding:
Farmer Brown has 10 sheep - 7 (X) were infected and recovered, 3 (O) still susceptible:
XXOXXXOXXO
If an Infected sheep (I) is introduced to the herd, it is most likely to bump into an X, rather than O.
XXOX
IXXOXXO
The Xs are protected directly by antibody immunity, so won't spread the disease. The Os are protected indirectly, due to herd immunity.
Farmer Green has a separate herd of 10 healthy sheep, all susceptible to disease. They're enclosed in a fence, but there is no herd immunity, because the introduction of a single infected sheep could get them all sick.
Now Farmer Green sells his entire herd to Farmer Brown. The new herd has 7 infected + 13 susceptible
OOXXOXOOOXOXOOXXOOOO
If an Infected sheep is introduced, it is most likely to bump into an O.
OOXXOXO
IOOXOXOOXXOOOO
We would say there is no herd immunity. The Xs are still protected due to their own antibodies, but the 3 Os that had immunity due to being in the herd have now lost that due to the introduction of healthy, uninfected individuals. One infected individual can get all the Os sick. It wouldn't matter if Farmer Brown's sheep followed a different religion from Farmer Green's.
So the question I think Lurker was asking was What happens if Farmer Brown and Farmer Green keep their herds separate, but all the sheep spend an hour a day foraging in the same field. Is this equivalent to the case where the two herds are combined? How much time do they need to spend together to be considered a single herd, when it comes to herd immunity?