Why should it accept "pet passports " that do not accord with EU standards?
Allowing animals unfettered access to mainland Europe without having any knowledge or input into the regulations of the country of origin
My understanding was that all existing EU law would be grandfathered to post-Brexit UK, so I don't believe the existing scheme will become (potentially) unsafe immediately as none of the UK's laws will change overnight - they will still be those into which the EU had knowledge and input, for some time.
A transition period to a new scheme would be needed, but I don't see a reason to scrap the old scheme before it's implemented.