Thucy,
You want to impose your own cultural norms on everything in sight, about everything you care about, and then leave the rest of the small cultural details and traditions to traditional cultures. That's your idea of everybody getting along.
To answer your question,
" Can't we just work to strip the bad from the good, keep the Jewish/Muslim/Irish/Kuridsh identities and strip away the bad things that come with that?"
No, you can't, if the Muslim (for example) identities fundamentally require things about civil law. You're just redefining their identities after your own mold.
Of course, I'm an American and very proud of the American system that, to some degree (though not the degree often believed) requires just that. But I don't pretend that it's consistent with the ideals that some other cultures are based on, and that there isn't a substantial cultural change being asked when I say that somebody coming here has to accept it.
That is, that tolerance and multi-culturalism is itself a *cultural* norm, not some neutral backdrop; and so, to the extent all those Texan immigrants you celebrate are abiding by it, and to the extent they're from places where it doesn't exist, to that extent their culture is more Texan and less their old culture.
"Do you also disagree with the concept of liberal secular democracy?"
As you would probably define it, yes. It inevitably ends up radically privileging uniformity and (substantive) secularism, to the disadvantage of all other cultural values.
I'm all for tolerance, though, and -- as you might suppose from my answer -- there are some definitions of the term that I would be fine with.