So they are just religiously Jewish correct?
Which is why, once again, Khazars or whatever you want to call them are uncommon.
Interestingly though, our new cantor is a Caucasoid Italian convert, so he isn't "Khazarian" but he could be considered it, even though he is a first-gen convert.
Of course, I could very well NOT be of direct descent, but I'm fairly certain my family has been Jewish for at least 2000 years.