The saying has always been a bit peculiar in my view. It gives me an impression of National pride, a bit of macho posturing, and the image of the snake. I figured the snake was the representation of something that, if you stepped on it, would whip around and bite you. Hence the warning, "Don't tread on me."
So I finally bothered to give the saying some actual thought and consideration. I came to a perspective that is a little different than the one described above. "Don't Tread On Me." is more than a tough guy slogan of National pride. It's actually a practical expression of how to succeed in a world of freedom and liberty. I am an anarchist. That doesn't mean spray paint, spiked hair, and using foul language talking to my parents. What it means is that I believe in the ultimate positivity of human nature. That we can govern ourselves. That we don't need to create entities to control us and limit our freedom in the name of order.
In the world I would prefer to live in, "Don't Tread On Me." would be a fundamental tenet. What it means is: Live your life, enjoy your freedom, just pay enough attention to your behavior to avoid stepping on me and my freedom. Critics often respond to this notion with the argument that in such circumstance, you aren't actually free. Bull fuck. I don't have time to sit around and argue semantic, legal-esque type arguments. You can be considerate and still be free. If you disagree based on semantic definitions, then feel free to go sit on a dildo and stroke your genitals; you ARE the problem.
Anyway, "Don't Tread On Me." is an individual and personal, philosophical expression of how we can enjoy freedom and liberty without fighting each other to assert our commitment to such values.