Pronunciation of "Einstein"
Why is Einstein pronounced with a s instead of sh, while the ei is pronounced ine?
This looks inconsistent.
First off, Albert Einstein's surname is pronounced with a sh sound in his native Germany, due to the second syllable of his surname beginning with "st" (literally, his name means "one stone"). The vowel grouping ei in German is pronounced similar to the English "eye", though with less emphasis on the first part of the diphthong. (See the Wikipedia entry for more details.)
As for the typical English pronunciation of his name ("ine-stine"), of the two parts that are not typical in English, one was retained when he migrated to the U.S. later in life, the other was not. Of the many German migrant families whose surname ended in -stein, some chose to keep the original ei pronunciation (-stine) while others more or less gradually switched to pronouncing it -steen for a variety of reasons. While the ei sound is of course quite easy for English-only speakers to pronounce, the sht sound is less natural.
As British English speakers (and please don't crucify me for saying this, see the disclaimer below) arguably learn fewer foreign languages than other Europeans, and even fewer Americans learn a second language, some pronunciations of foreign names are gradually adapted, and sometimes the spelling is modified to make the name "less foreign". (I have wondered many times whether it is worth the battle to continue insisting that my Germanic surname, which ends in -mann, keep its second n at the end. Many an authority or government agency has gotten this wrong and it has caused me some major headaches.)
In Einstein's case, I can only assume - and this is pure conjecture on my part - that because he became well-known in the U.K. and U.S. long before his emigration, people's minds about how to pronounce his surname were made up and he either did not mind, was too polite, or simply gave up trying to correct them. My point being that changes in spelling or pronunciation of migrants have little to do with consistency and far more with convenience.
Disclosure/Disclaimer: this post has been heavily edited after a bashing for being "baseless, biased, and not helpful for answering the question". Though I live in Australia, I'm a native speaker of both English and German (as well as one other language), have learned a couple of others well enough to muddle my way through a conversation, and have a very basic understanding of a few more. Please don't think I'm stating my linguistic background to brag or to claim to be an expert on linguistics (my sister is the one who has a Ph.D. in linguistics), nor that I intend to offend anyone when I say that English speakers typically learn or speak fewer foreign languages than native speakers - and yes, I do realise that frequenters of EL&U do not represent "typical" English speakers. I am also not judging this imbalance of foreign languages in any way, I will happily leave that to others, some of whom are far more prominent than I.
The pronunciation of foreign words comes from different sources.
If all one would ever know is the sound of the word (that is, without writing), hearing it from foreign pronunciation, the foreign word would still be heard with what is expected locally, ignoring distinctions present in the foreign word (most people do not pronounce the tones that a Mandarin speaker would in 'Beijing'), and creating distinctions that just weren't there (likewise, most English speakers pronounce the 'j' as the 's' in 'measure' which sound is not in Mandarin. And then the word would be pronounced using the native phonetic inventory and expected patterns.
And then most people learn foreign words through writing rather than hearing them directly. There are rules of orthography, what maps the combinations of letters to sounds. English is notorious for having inconsistent pronunciation rules, or an excess of idiosyncratic ones (cf. the 10 ways of pronouncing '-ough'). Also, education and standards can help enforce some things. Most people will pronounce 'hyperbole' closer to the original because education has provided an exception to the silent 'e' rule.
All these will interact in fairly complex ways, some reinforced by local culture.
This doesn't mean that anything goes but rather that as much as one may try to faithfully pronounce foreign words, there will be many forces that will pull in multiple directions.
As to 'Einstein', it is spelled the same in both German and English. The common letter sequence 'st' in German is pronounced /ʃt/. The same sequence is pronounced naturally as /st/ in English, and even though the German version is easily pronouncible in English, it is just not as common.
As to the vowels, 'ei' is usually pronounced /ay/ in German. But as to English, there are many ways to pronounce 'ei': 'their', foreign', 'eight', 'height'. It is pretty reasonable to be able to pronounce 'ei' close to the German /ay/.
These are just ideas. There's no proof that a particular orthography must have a given pronunciation (at least not in English). But these are plausible justifications. Though culture trumps most everything, I'd say that the English way is just the natural wasy according to English orthography, and that explains enough why 'ei' is maintained as the original language but 'st' is not, in this one single word.
Inconsistency often comes from the natively English orthography, but in this case it is simply the different orthography rules between German and English.