My partner and I just returned from a cruise that started in Rome and ended in Istanbul and we experienced no problems of a threatening nature at any of the ports. Neither did we hear of any problems from any fellow travelers. The worst problem was the agressiveness of street vendors in Turkey. While being very pushy in vending their wares, it was in a friendly manner.
Go ahead and enjoy the trip and hopefully you will encounter no problems and will return home with the desire to return to these ports when you can spend even more time.
Happy cruising, Robb