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You can be an Asian Jew - by bloodline or by conversion.

So Jews are more of an ethnicity then a race, and again, it's not the Rebbenute doing the genetic studies to prove that one way or another. The Lubavitchers never turn anyone away, Jewish or otherwise, and they're the largest movement of Hadisim in the world right now.

It's the Ultra-Orthodox who have a monopoly on conversions recognized for Israeli citizenship, but the restrictions are not that different from other nations like Jordan. The acceptance of conversions is a denominational thing, and depends on region, sect, etc. without consistancy over history. The only time it becomes an issue for some Rabbis is when you want to get married, have a bris, get a divorce, make up a minyon at a synagogue.