Honestly, Japanese anime characters do not look western to me. They look Japanese, but that's probably because I'm used to seeing them in anime! I don't see how classic Japanese drawings have anything to do with it; different styles of drawing grew up in different cultures, I expect, and not just because of the different look of people from those culture.
As for the baseball question, I don't think it makes much sense. Soccer is popular almost everywhere in the world except in the United States, so it's obviously not a Western thing, and there are other sports highly popular in some countries and not in others. It has more to do with history than with any fascination. For example, cricket and snooker are extremely popular in countries that used to be parts of Great Britain, but that's just history, not any "worship" of England.
Small correction : Great Britain refers to the group of islands also referred to as the British Isles. Great Britain is a geographical reference. The full name of the UK is 'The United Kingdom of Great Britain and Northern Ireland'. Hence 'British' is a generic term for anyone from the British Isles, although it tends to be used to describe English people, though technically Welsh and Scottish people are also British. This is similar how 'American' refers to citizens of the United States, even though technically anyone from Alaska to Argentina is American.
So you can't be a former part of Great Britain unless there is some major tectonic activity!
The correct term would be 'former British Colonies', or perhaps, beter still, 'former members of the British Empire' or even 'Commonwealth nations'. Even these have problems because most of the Northeast USA was once part of the British Empire. And, curiously, Canadians never really went for Cricket despite still being in the commonwealth. I guess it's difficult when the fields are under snow for half the year.
Your point stands - cultural traditions can take root in any place, and don't necessarily imply a worship of the parent culture. It probably has more to do with a filling a cultural need with a pre-created product than anything else. You could reverse the trend and ask why so many young people are into the 'import' car scene : which generally means Japanese cars. Is this a worship of Japanese culture or just young people finding that Japanese performance cars are cheaper and more accessible?
The comment wasn't meant to be nitpicky and irrelevant. Was just meant to be an interesting sidebar into the discussion of the term 'Great Britain'.
I guess I should have used a different tone or something. All my other comments I've done expanding something like this have generally been well received, so I'm at a loss why this one was taken so badly. Maybe it was the parent thread.
No sure why this is downvoted - it's correct, and it appears that the parent is confusing Great Britain and the former British Empire (where the popularity of cricket is widespread).
As for the baseball question, I don't think it makes much sense. Soccer is popular almost everywhere in the world except in the United States, so it's obviously not a Western thing, and there are other sports highly popular in some countries and not in others. It has more to do with history than with any fascination. For example, cricket and snooker are extremely popular in countries that used to be parts of Great Britain, but that's just history, not any "worship" of England.