I think the question you are posing is as fair as asking an American, or a Canadian, or a Frenchman, etc. to convert to "Hellenism" or to become a "Russophile" as a pre-condition to their hearing and accepting the Gospel.
I dont expect the American, or Canadian, or Frenchman to Give up their Culture and 'convert' to Hellenism, but I do expect them to embrace an Orthodox Culture, and allow it to influence their life. Does this mean that they have to abandon the culture they were born into? No, of course not. Does it mean that they should respect and appreciate Orthodox Culture, and recognize it has many important elements for a Christian life lacking in their own? Yes.
Concerning the words of Paul, he was speaking on a personal level, about what extents he goes to inorder to spread the Gospel, he's not telling the Church to change to conform to society. Are we to infer from his statement that he is telling the Church to be both under the law and not under the law? For that is the conclusion if you take the approach that this passage is an instruction on how the Church is to form its Doctrine and Culture.
I think it would be fairer to ask whether those who have a "radical and violent reaction" against Churches celebrating services at least in part (or some of the time) in the vernacular of the lands they are situated in, are the ones treating the Church as a sort of "social club" with some smells and bells.
Generally those who convert to Orthodoxy (at least for reasons other than marriage) do so out of conviction. IOW, if they didn't want to be there, they wouldn't be; for them there's no possibility of it being an "accident of birth".
While it is true that those who convert to Orthodoxy do so out of conviction, I often wonder if this conviction is always for Orthodoxy and the Truth. Too often have I heard arguments from converts who use a few proof verses and out-of-context quotes from the fathers to contest a custom or doctrine that the Church has accepted for well over a millinium. So while there is a conviction of something when one Converts, often these converts just find Orthodoxy closer to their beliefs than either Catholicism or Protestantism, and rather than comming into the Church, and letting it change them, and accepting the Church's grace in Humility, they come into Orthodoxy trying to change the elements of the Church that dont fit nicely with their beliefs and preconceived notions of how the Church should be.
There is another advantage that those born into an Orthodox Culture have over we converts. While most converts came to Orthodoxy on account of either an academic acceptance of Orthodox Dogmatics or Ecclesiology or after having an attraction to our ancient services and customs, those who are born into an Orthodox Culture come to the Faith by far more natural means, it is simply part of their life, part of their world view, part of their identity. Moreover, this also sheds some light on why certain Orthodox, especially those who are from an ethnicity that is Predominately Orthodox, react the way they do to the loss of their Language in the Church; for Language is an integral element of Culture, thus it is part of their life, world view, and identity, when the language is Changed, they suffer a loss of culture, a loss of identity, yet one more sphere of their lives that our Materialistic culture has inflitrated, they are alienated in their own Church. Can language change? Yes, just as culture changes: slowly, and with time, as the Orthodox Culture adjusts to the new circumstances it finds itself in; and, of course, the rate of change will vary with each parish (but I'm talking about maintaining the status quo
until a consensus, not majority opinion, is reached).
An example of this that recently came to my attention is in England, where Orthodoxy is considerably more ethnic than in America, a certain, fairly ethnic, parish that had previously had all Liturgies in 95% to 100% Greek, introduced a Sunday Liturgy, predominately in English, once a month. This was done primarily for the benifit of the second and third generation children of immigrants, the idea was approved by the Archbishop for a six month trial, at the end of which the situation can be evaluated. Because there was a consensus on this issue, and the way the issue was approached, the problems that ensued were minimal, with very few complaints, and this even had the support of the most Greek members of the Parish, who were actually from Greece. I, of course, cannot speak for them, but I would guess that the change was accepted and even embraced by nearly the whole parish because it was not made in a threatening manner, the goal wasn't to eliminate Greek Language or Greek Culture from the Parish by any means, no one was trying to 'Anglicize' the parish, there were no hidden agendas, and no one (i.e. converts) trying to undermine the Greek elements of the Parish; but, rather, there was a concensus to help educate the Children of the Parish. If it accomplishes such a goal, and does not cause division in the Parish, then great; if it fails to accomplish anything or does cause division, the situation would need to be re-evaluated. This is the manner in which change can be made, slowly, with the primary concern being the maintaining of the flock, and the prevention of scandal.
This is the same rationale used by the early Judaizers - "it's ok if you want to join us...but first, become a Jew". Obviously the culture from which missionaries come is going to rub off in some wise on the sensibilities of their converts - the marks of semitic culture are still apparent to this day in all flavours of "apostolic" Christianity (for lack of a better term), as are qualities specific to Byzantium in what became a distinctly "Slavic" Christianity.
As Anastasios has rightly pointed out, the various Slavic cultures (and earlier, those of the Romans, whether eastern or western) did not start out "Christianized" either.
The issue with the Jews was actually a matter of Incarnational Theology and Soteriology, and the subsequent relevance of the Mosaic Law: Acts 15:1 ('And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved.') demonstrates a doctrinal dispute, not merely an issue of Culture. A doctrinal statement is not the issue being considered here, a way of life is: No one is saying, 'except ye learn greek ye cannot be saved;' what is, however, being said is that Hellenism has a special relationship to Christianity that cannot be found in American 'culture.' Also, I will add that Hellenism, like Semetic Culture, has a relationship to Christianity that no other Culture can ever enjoy: it was Greek Language, Greek Thought, and Greek Philosophy that was used to define the fundamental doctrines of our faith, and it was Greek Culture that was used to propagate it throughout the world. And while it is true that no people or culture are completely deprived of grace, I do believe that the individualistic American society and culture are further from Christianity than either pagan Greek or pagan Slavonic cultures were when Christianity came to them. Our culture, on top of being individualistic, tends to propagate a rationalistic weltanschuung that is both less accepting of and less consonant with the precepts of our Orthodox Faith.