It is always and has always been a mystery as to whether someone can be Jewish in ethnicity but not Jewish in religion and vice versa and it has never been explained adequately. So right now it is fine to say that those who convert to Judaism are considered part of the Jewish people without classification.
Based on the bible, everyone who converted to the Jewish God was considered a Jewish. So yes, anybody who wants to be Jewish and is converted should be considered Jewish in my opinion. Just like Christianity new converts and other religions around the world, so can people become part of the Jewish race.
Yes, people who convert to Judaism should be considered part of the so-called Jewish race, because the people who converted during Bible times were certainly considered. God saved the people who chose to fear Him, whether they were Jew or Greek. Thus, everyone who believes in Judaism is Jewish, and acknolwedged as such.
Be considered part of the Jewish race but they should be able to be called a part of the Jewish religion if that is what they believe. Race and religion are two different things and you cannot truly become a part of a race just by changing your religion, then again it depends who is considering them to be part of the religion or race.
Jews aren't a race--period. Hebrews are a race as they came from one of 12 tribes that settled in what is now Israel in ancient times. Hebrews share a common DNA and common language. However, Jews are a religious group and not a race. Are Muslims a race? Are Christians a race? Are Hindus a race? Then Jews are not a race.