Is it socially acceptable to punch the poor and mentally deranged?

About an hour into Assassin's creed, I'm constantly either being pestered by poor people for money, or being pushed around by a mentally unstable person (for no reason other than being in their way). I know that killing the innocent is against the creed, but what about punching?

Since I encounter a lot of these folk, I'm wondering: can I punch these people/grab them and throw them to the ground without raising my alert level (i.e. will my status change to red and will people start calling me an infidel)?

Also, since killing a certain number of innocents causes the Animus to reinitialise after a certain number of kills, does this apply to hitting people? Can I punch as many people as I want without fear of reinitialisation?

Hitting people won't get you desyncronized (unless you beat them to death, which takes more than 1 strike), but it will cause guards to harass you if they witness you doing it. You'll need to run away or take to the rooftops to avoid beggars and lunatics without attracting undue attention.

You can bump directly into poor people a couple times, which gets them off your back without attracting attention.

It's best to simply avoid mentally deranged people, which is easy to do given they are rather slow and do not chase after you. If needed a single punch will make them run away, but it is not considered 'socially acceptable'.