There's a lot of talk that gets tossed around about protecting our mesorah, but <ר> still gets pronounced as /ɹ/. I think this is in many ways an inevitable thing. As much as people might have you believe that proper pronunciation is a halachic issue, it seems that communities have adapted their havarah to their linguistic framework — consider the Ashkenazic loss of pharyngeals.
In some ways the evolution of liturgical pronuciation seems to parallel language loss over generations. With language loss in the US, a common situation is that the first generation speaks the language fluently, the second passively and with somewhat sub-par pronunciation, and the third in a rudimentary fashion, if at all. Similarly it seems that Hebrew pronunciation has gradually shifted in the US to accommodate English phonology, both in consonants (/r/ in particular) and in vowel quality (note especially the fronting and dipthongization of /o/).
What has puzzled me is that this does not seem to be absolute. Jews are known for being able to pronounce /x/, and among religious (or at least somewhat motivated) Jews this does not seem to be disappearing. I can see a few possible explanations:
(1) This sound is used in a few English words ("Bach", "loch", "ugh", "Hannukah"), although this seems tenuous.
(2) Unlike /r/ or /o/, /x/ must be preserved to avoid collapsing minimal pairs (e.g. כל/חול, לכם/להם). This seems more likely, although the historical loss of pharyngeals precisely lead to such a collapse. (By the way, I am curious about how successful the younger generation of sfaradim in America is at pronouncing such phonemes. Feel free to let me know.)
(3) Perhaps /x/ sounds different enough from whatever sound Americans might collapse it into (/h/ or /k/) that this process is blocked.
I also wonder if there are other examples, in Hebrew or in other liturgical languages, of phonemes being preserved that are not present in the local spoken language. The only other possible example I can think of off the top of my head is the /œ/ of Temani Hebrew (although maybe some spoken Arabic dialect had that sound; again, let me know if I am wrong).
At some point in time I might research this topic and write a more conclusive post.