I think this is very dependent on what you're actually doing. I'm involved in an attempt to bring some more sustainable/regenerative methods and technology to agriculture, and in that space I'm glad to see anybody show up who's doing the same. I don't have competitors (in my view), because I have a gigantic task in front of me and my main concern is to see that it gets done (even though I'm trying to make money on it at the same time). I go out of my way to help other people who are trying to make a buck in my space.
On the other hand, if you're selling a commodity (e.g. gasoline), then it's pretty hard to say that the guy across the street isn't competition. Perhaps there's a spectrum of appropriateness for cooperation/competition between these two extremes?