Tricky subject this, but I support the sentiments expressed by istanbul bisiklet motosiklet.

What I've learned when inadvertently entering a protest area of some sort in Turkey, the Middle East and South America, is to observe the protesters first. If there are families with young children, or more so, babes in arms or on backs, then it's likely to be pretty safe and friendly.
By whatever means possible, dress or behaviour, make it obvious you're a tourist. If any local people feel danger is lurking, you'll be looked after, which might mean strong advice that you leave the area. Best not to ignore that.
If the crowd seems to comprise mainly family groups then again it's probably safe. If there are large organised-looking groups seeming to be 'on a mission', maybe not.

From an experience in Peru, if you get the slightest indication that tear gas may be used, get somewhere safe. It's pretty nasty and drifts with the wind to wherever the wind is going, which may be away from the dodgy area. (In this case, towards the hotel I was staying in!)
I missed the early warning, but will remember in the future. Quite a way away down the street, people were suddenly acting strange - wrapping scarves or handkerchiefs around their faces, crouching low and running. I had not the faintest idea what they were doing, but soon enough found the wind was drifting my way. I learned if I see that again, run at 90 degrees to the direction of any wind, or the same way as everyone else!

Back to the poster above, as a Middle-Eastern example, about 15 years ago I was in Istanbul with my daughter, aged about 17. We wandered into the area close to the book market, which I wanted to visit. She didn't and just wanted to find somewhere she could sit and 'people-watch' while I went off.
Well, there were plenty of people to watch. A pretty big protest about government plans in those days to secularise the country. It was a big student protest, massive banners everywhere but with a very overt party mood. So it seemed safe, we found a large mosque on the edge of the protest area with worshippers coming and going without problem. But from there we could see, parked away from the area, ranks of massive water cannon, armoured vehicles, armed personnel, more than any I'd ever seen in a big city. But they all seemed bored to tears.
My daughter felt confident it was safe for her to sit on the steps of the mosque while I went to the book market, and there were lots of people around who obviously had nothing to do with the protest. And we probably looked like tourists.
So I went off, found I could see the edge of the protest area from the edge of the book market, and spent quite a while there.
I returned after over an hour to find my daughter in deep conversation with two young girls, student protesters, in muslim dress and headcoverings. They had approached my daughter as soon as I left and spent the whole time explaining to her the history of the government's policy, the opinions of the students, what they hoped to achieve and lots of other stuff about Turkey and Islam. They introduced themselves to me and talked some more for a little while.
Since then my daughter has been able to travel and work, alone, in middle-east countries confident that she understands the cultures a little more than many foreigners, and has never felt in danger anywhere.
So it's one of those tricky things, deciding when to get into a bit of 'adventure' for the huge education and experience it can bring you.
And I'd repeat, the biggest thing I've learned in these situations, is always make sure you look like a tourist......

From my own trips through Muslim countries, and my daughter's (she's done more), EVERYTHING you read and see in the UK mainstream media will be 100% misrepresentation. A great pity.

Lastly (I hope) I just remembered, a pretty good book about adventures to be had in North Africa if you're travelling as a sort of family unit, is "Hideous Kinky."
(DVD as well I think - not seen it - book is probably better. But no motorbikes if I remember right).

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TTR250 - London to Cape Town