Istanbul is definitely a safe spot for Jews, unless you are in one of the hard-core Islamist neighborhoods like Ismailaga, wearing a kippah on your head. I'm not saying that something will happen to you for sure, but you may get insulted. Here is an article of a Turkish journalist, Ayse Arman, talking about her experiment in Istanbul. She is actually a very liberal woman, but she wears a hijab and goes to liberal neighborhoods to check out the reaction of people -it's fine-, then she wears a mini-skirt and goes to Ismailaga Neighborhood. One of the long bearded men in the neighborhood tells her and her friend that they are just a piece of shit. Of course, they jump on the cab and run away.
Basically, if you are not being Bruno in Jerusalem, then you'll be good in Istanbul. You'll see how friendly Turkish people are. I've been talking to many travelers to be able to understand their Istanbul experience better, and I heard that many of them were really surprised after realizing how friendly Turkish people are.
Don't get me wrong. There are people who are taking advantage of this, and trying to scam, or sell more stuff to tourists by "being" friendly, but if you are being smart, then I think you can understand the difference pretty easily.
You should definitely have a Jewish Heritage tour in Istanbul.