To Anglicize or Not to Anglicize?

Shuttling back and forth between both academic and ‘regular’ life in the US and the UK has made me aware of a significant difference between Yanks’ and Brits’ inclination to Anglicize foreign-word imports into the English language. One of my first hints as to the existence of the difference was when I realized that the dish that Americans pronounce ‘fil-ay of sole’ is standardly pronounced in England ‘fil-et of sole’. Gradually, I realized that this divergence pervades American and British English. I especially was struck by it when it comes to the pronunciation of foreign names. I recall eating breakfast, at a conference in Wales, with two British academics, both of whom are well-respected scholars in the history of political thought. As I listened to their conversation (with little to add of my own), I grew puzzled at to just who was this Italian political theorist ‘Russo,’ whom they kept mentioning, and with whom they seemed to assume I was familiar. When one of them brought up the story of ‘Russo’ sitting on Hume’s lap and crying, it dawned on me that they were talking about Rousseau! When I asked them if this was so, they looked at me as if I was quite daft, since I was saying just the same name that they had been.
Once I had identified this tendency, I was, at first, quite bothered by the British practice, and was sure my American ways were to be preferred. Why, here was a renowned figure in the history of political thought talking about ‘Gee-an-battista Vico’, when I knew he should be saying ‘Zhan-battista Vico’!
But then, listening to a series of lectures on the Axial Age by an American scholar specializing in Indian religions, I found myself growing increasingly annoyed at his use of esoteric Sanskrit and Pali pronunciations of names and terms that are fully incorporated into English with Anglicized pronunciations, e.g., his saying ‘Buh-DA’ instead of ‘BOO-da.’ And that made me realize that the issue wasn’t as straightforward as I had initially assumed. While there are cases where it is obviously better to use the anglicized version of a foreign name (imagine listening to a lecture by an historian who kept saying ‘Kikero’ and ‘Yulius Kaiser’ instead of ‘Sisero’ and ‘Julius Siezeher’) and others where Anglicization would clearly be absurd (after all, even the English say ‘chow,’ and not ‘see-ay-o’ when employing the Italian salutation, and ‘wee,’ not ‘oo-ie,’ when saying ‘yes’ the French way), there are many other cases where the correct choice is not so clear cut. When the professor who taught me history of science (an Englishman, by the way!) would say ‘Ein-shtein’ rather than ‘Ein-stein,’ was he being overly pedantic or just faithful to the native pronunciation of that scientist’s name? If I insist on saying ‘Zha-notti’ rather than ‘Gee-a-notti’ when discussing the Florentine political theorist, am I showing off or being accurate? (And just why is it that Americans say Rudolph Giuliani’s name in (semi) Italian fashion, with the initial ‘i’ being silent, but, when confronted with the very same construct of Italian spelling, always sound the ‘i’ in ‘Giovanni’?)
It may be that there is no clear answer to these questions, other than ‘If everyone laughs when you say it one way, you’d better say it the other.’ But I seek your input: can anyone out there propose a reasonable rule as when to Anglicize and when to not do so?