I suggest you read
Albion's Seed: Four British Folkways in America by David Hackett Fisher.Most likley the best book on the traditions and difference in the founding groups of America.
I've never met an Anglo-Saxon Protestant who wasn't "white" so I guess you could call them an ASP. Well let me correct myself I've known people who are very Anglo-Saxon in their culture, but their ancestors were not "white "but they had him been raised in England for generations. There are plenty of Anglo-Saxon Roman Catholics as well. They are y Anglo-Saxon insofar as their particular cultural and linguistic traditions,thye have chosen himor themsle him ves.
Of course I got sucked into the white thing, white should be abandoned for some other term like indigenous Europeans. I myself am a Buddhist great respect for traditional Japanese culture and Chinese culture and for that matter Indian culture.
As for your question but what real cultural differences? The answer to that would depend upon how you define real cultural differences.
That would be entirely subjective unless one were to set out some sort of precise sociological criteria for defining the groups. Although the great diversity for lunch bunch would like you to believe you were all going to meld into one identity it certainly hasn't happened in the UK, or even in Europe.
Being that my grandmother's people are from Northern Ireland and having spent a good deal of time there as well as in Wales ,Scotland and the Yorkshire Dales I have seen definite differnces in each groups worldview, disposition, and what they consider valuable, what they don't. Not to mention the differences in dialect.
The differences are real enough for the people that the dissolution of the United Kingdom into England, Scotland and Wales is a possibility.