Dogs aren't a native species and can in fact be ecologically damaging. Squirrel population control is a question beyond my ability. Butterflies are both native and useful. Hopefully this is helpful.
No it's not, your local tennis park has no ecology to speak of that could be disrupted by dogs. You just don't like dogs and instead of stating that you want your preference imposed on everybody else just because it's your preference, you have a list of dubious reasons why dogs shouldn't be allowed here or there.