Hi, Jim —

Perhaps they are of Jewish extraction, either:

• a Jew
• a Messianic Jew, or
• a Hebrew Catholic, for that matter, meaning:
  
  A Messianic Jew is a Jew who has accepted Jesus as Messiah; basically a Christian of Jewish heritage.

Also, Galatians 6:16 suggests that Paul considered the Christian Church to be Israel in a sense,
a theme he discusses in Romans 9:8 and 11:7-27. As Pope Paul VI said,

"We are all spiritual Semites."

But I've never heard anyone jump from this to calling themselves Israelites.

Eric

Jim —

The Israelites are the descendants of Israel (Jacob), and were known by others as the Hebrews.

The Israelites always allowed conversions from other peoples and assigned them to a tribe.

Mary Ann