see if you can work something else out with them(other security questions, ie mothers maiden name, last 4 of social, etc.)
I have never sent my ID to anyone I did not know, not being too cautious imo, but being smart about who I share personal info with. There is too much identity theft in the world to be careless with your personal info.
I have account at over a dozen books, and there isn't a sportsbook on the planet that has my ID. Any that asked for one was told no and we worked something else out. I understand that they are doing this for "my safety", but I'll tell ya what- I'll take care of myself by keeping my sensitive personal info just that.