I usually wear 2 diamond rings.Should I leave them at home when visiting Istanbul?
No more than any other place. You're more at risk wearing those in the states that you are in probably any European country.
I have a very thin wedding band that I wore when traveling in Europe and left my wedding ring in our safety deposit box. My advice is to not bring anything that’s either sentimental or expensive.
I had to remove my earrings during my trip last month during a TSA check in Europe (they weren’t the cause). I quickly put them in my purse afterwards in the phone pocket, and I lost one of them in the airport. They weren’t expensive or sentimental, but I was still bummed. ; )
The only times my wedding and engagement rings have left my finger was for surgery. And even then it took effort to get them off. I suppose if one or both had particularly large diamonds, I might turn the ring so that the stones were palm side, when I was out on the streets. But I've never found it necessary.
If you never take the rings off, I think you’d be fine. I can’t sleep in any jewelry, so I take mine off at night. I don’t take any jewelry that I would be upset if it were lost or accidentally left behind.