Generally law officers here apply laws against civilians based on preventing harm to others. If you have a wine bottle in the park and a officer walks by, they most likely wouldn't do anything. If you're loud and obnoxious, they would do something as you're disturbing others.

Seemingly the police here are of the view that most dogs don't pose a threat to others and are not annoying when off leash, as I haven't been confronted when walking next to them with my leashed dog.

Carrying a gun would obviously not be OK here as it's strictly outlawed. If I went to the US, I would probably feel the same way that some feel against dogs here but regarding guns, so that's actually a good point, thank you.