They also claim the documents could herald a "surveillance state".
The message is contained in an open letter from ministers from a number of different Christian faiths.
As lockdown restrictions ease, the certificates could play a role in allowing the safe reopening of theatres and nightclubs.
Significantly, however, they have not been included in a series of pilot projects of large scale events due to get underway shortly.
In the letter the group say introducing passports would create a "medical apartheid".
They add: "This scheme has the potential to bring about the end of liberal democracy as we know it and to create a surveillance state in which the government uses technology to control certain aspects of citizens’ lives.
"As such, this constitutes one of the most dangerous policy proposals ever to be made in the history of British politics."
The ministers also threaten to ignore any potential restrictions which would ask them to refuse entry to their churches to anyone without a vaccine passport.
Mr Johnson is also facing a significant rebellion over the idea from his own backbench MPs.
More than 70 Conservative MPs argued forcefully against the proposal earlier this month.
Labour leader Sir Keir Starmer has also said he is "very worried" that the certificates could be used to discriminate against those who have not had a jab.
Critics of the policy argue that it could backfire and that it is better to encourage those hesitant about vaccinations to get inoculated, rather than punish them with a system of passports.
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