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Make lots of eye contact, smile and be open about what you're doing. If they seem uncomfortable, back off.
Whether people demonstrating mind you taking photos or not often depends on the general mood. If they're trying to be inclusive, they often won't mind, as they generally recognise photographs are part of how they get their message out.
If they're spoiling for a fight, on the other hand, they might use the excuse. If you feel the mood turn ugly, check your exits, and if you're not sure you could stay out of harm's way if they did decide to have a go, scarper.
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Like others have said, protests/demos are some of the easiest places to get up-close street-style photos of people. It's pretty much expected that there will be people taking pictures (these days, they seem to outnumber the protesters).
Just be aware of the mood and try to blend-in.
Also, keep an eye on the police – stay out of their way if it's a bit rowdy.
Any tips for street photography - specifically getting personal feeling shots at protests/demonstrations/mass gatherings etc.?
There is a small local protest near me tomorrow that I thought might be good for the photo comp, but I've never taken photos in that kind of environment at all. I've never really done any 'street photography' and in fact I barely think i've ever even taken people focussed photos where the subject wasn't known to me. Really inspired by @Well_is_it a page back and some of Mr Melling's stuff but it's a side of photography that I've never tried before.