An explanation that possibly works for most of it: in the new history, the 3 main earths (Arrow/Supergirl/Black Lightning) have all been one earth. However, in this history there were other earths and a revised version of the Crisis occurred that wiped out those other earths as far as they know. They are unaware that some were saved. So, Laurel and Nash are still from other earths, just earths that were destroyed in a post-Crisis version of Crisis as opposed to being re-written as never existing. And, it was this version of Crisis that has screwed up much of the physics.

However, Cisco should have both sets of memories (or multiple sets, as this is not the first time his past has been rewritten) and thus remember owning a Superman t-shirt. I think he should be freaking out more just from the existential crisis of there once being multiple Ciscos across the multi-verse and how does he know which one he really is? Who's to say that not more than just 3 earths were merged and he maybe a conglomeration of a bunch of different Ciscos. Should he think of himself as the Cisco from pre-Crisis or the one who has lived his whole life on the post-Crisis world?

It's kind of weird because the Pre-Crisis Cisco did die in the Crisis along with everyone else from Earth-1 and this one is technically the Cisco of the Post-Crisis world, but he thinks he's the Pre-Crisis Cisco because of J'onn altering his memories.

Laurel and Nash shouldn't even exist anymore, but then Supergirl and Batwoman have had people from other Earths suddenly showing up on the new Earth.