Welcome,
I assume that everyone here possesses common sense. Whether you reside in or visit the vibrant city of Edinburgh, you're likely to encounter tourists engaging in typical tourist activities, capturing moments with photos and selfies. Similar issues are reported across Europe.
This phenomenon is prevalent in my travels, be it in Buenos Aires or various cities in Brazil, Peru, and beyond. I've received warnings about carrying my phablet in a belt holster, wearing my daypack on my back, and using a point-and-shoot camera.
The key is to apply common sense. Upon arrival, observe your surroundings and ongoing activities. Pay attention to how people are managing, and take note if any issues arise. If you witness individuals having their phones swiped while in use, exercise caution before doing the same.
Remember, despite taking all the right precautions, unexpected incidents can occur; that's life. In my travels, I only carry items I can afford to lose. My passport and camera memory cards are the most crucial possessions, with my phone having everything backed up as PDF files in my email.
When using my point-and-shoot camera, I secure it with the wrist strap around my wrist—not just for theft prevention but also in case I accidentally drop it. This habit is a remnant from my SLR days. Similarly, if I have an SLR/DLSR, it's around my neck, ensuring it won't go far if dropped.
You might observe people with SLR/DLSRs around their necks taking photos, while others use their phones for selfies. Others may share additional advice, but I wish you the best of luck.