They are both made up registries that were only made up so that unscrupulous breeders could register their pups, meaning they could bump the price up on their previously un-registerable pups.

If the two registrations do not mix then why did they breed the two together?
I would walk away, why do you want a dog destined for a life of discomfort? These dogs are conformational train wrecks which leads on to many issues as they age.

 

Will they loss there regeneration like they are saying

 

You would have to check the rules for these kennel clubs themselves. One is UK based, the other US based.
From a brief peruse of their sites, I don't see anything that says a dog can't be dual registered. But I didn't look that hard. I'd guess you could probably register a hissing cockroach with either registry and they wouldn't bat an eye.

If the breeder is giving you the run around with papers that's a red flag to me. Among many others.
Why are you so concerned with registration? Are you planning on breeding your pup?

 

As StormyThai says both of these are 'fake' registries, they are just 'club membership' neither are recognised anywhere in the world by any offical kennel Clubs.

Any dog of any age, breed or cross breed can be registered with the DWKC

The ABKC currently accepts UKC, AKC & ADBA for American Bullies; BBC for Shorty Bulls and AKC, FCI, NKC, ABRA and IOEBA for Bulldog breeds

BOTH have got websites to sell their fake KC registrations, so you can read through them and see for yourself