Having two different pub schemes makes a mockery of the passport anyway as the people in the 2 different pubs will be mixing in the street,taxi rank,kebab shop,trains etc.
The vaccine pubs will be more like some sort of exclusive VIP vaccine only members club while others in society won't be...
I am having the jab but I would still be boycotting the pubs that adopted the passport.
I don't see it as an anti vaxx issue it is a civil liberties issue inter-twined with the rise of big tech companies.