i've never had to deal with protests on a mass scale, but frequently have to deal with neighbours protesting. The strategy I use to deal with it depends on my mood and the other persons approach. If they approach in a reasonable manner then I generally respond reasonably. The tight tree laws in australia mean that it's difficult to cut a tree down just because you want to so I explain the reason, which is often rot, disease or structural problems coupled together with a poor location - over a house or childrens play area etc.
It's not hard to deal with people who are really just being absurd so long as you keep your sense of humor. Here's some actual conversations between neighbours and me;
n:"oh my good what are you doing stop! you can't cut that tree down!!!"
m:"did we have to go to that tone straight away? couldn't we start with 'hello', or 'good morning?'"
n:"I want to speak to your boss immediately"
m:"I am the boss."
n:"why did they cut that tree down?"
m:"it was rotten and was never going to bounce back. It will just get more dangerous"
n:"well I want it back!"
m:"no problem, I'll just pop her right back in there"
n:"you can do that?"
m:"no."
n:"That tree was shading my house! We need to have trees in our neighbourhood"
m:"I notice that you don't have any trees in your own yard"
n:"well, I just don't have the space. I need somewhere to park my car"
m:"maybe you could offer to pay your neighbour to grow a tree for you"
n:"but that will take years! it's going to get hot in my house in summer"
m:"oh, don't worry about that, they're putting a block of apartments in here. There wont be a lot of light hitting your place."
n:"you must tell them not to cut that tree down! That tree is very special to me. They'll listen to you!"
m:"I totally agree with you. The good news is they agreed not to cut it down"
n:"wow, thats great news!"
m:"so, where do you want me to put it"
n:"what do you mean?"
m:"they agreed not to cut it down, but they can't have it in their yard. They're happy for it to be transplanted into your yard though. They'll contribute the money that they were going to spend on removing it towards a transplant if you pickup the balance of the tab"
n:"I can't have that tree in my yard! Look how big it is!"
m:"don't worry, it will only cost you a couple thousand dollars"
n:"a couple thousand dollars! for a tree!?"
etc etc...
Shaun