Not to mention, the Martian colony would forever be far far more frail to attack than any Earth society, since it has to spend so much of its nature wm resources just to keeping humans alive.
It's not entirely unlike an overseas colony in an inhospitable but not empty place. Start small and dependent, develop the land around you and become autonomous.
Of course the "other" cause may be to make a backup of the Earth civilization and humankind for a case of collapse on Earth, due to global warming, an asteroid impact that hasn't been averted, etc. But this is only possible with true material independence, such that can withstand any blockage or embargo from the Earth's side, else it won't stand the collapse on Earth. The colony may declare allegiance to a particular Earth's government, and inherit the civil norms from the culture(s) which built it, but cannot and must not be ruled from Earth.
Independence != animosity and bitter confrontation. It's more like Canada is independent from the UK, despite some formal allegiance, and the UK is not going to send troops if the Canadian parliament votes in a way that bothers the English monarch.
This is a colossal task, likely not achievable even in this century with the technology we currently have. Stuff like high-temperature atomic engines and other near-sci-fi stuff could alter the equation somehow.
But, if Puerto Rico wanted to become an independent nation, do you imagine the USA would let it without trying to quash the "rebellion" with both economic and military might?
The US did it for the Federated States of Micronesia, Palau, and the Marshall Islands in recent-ish years, why wouldn't they do it for Puerto Rico if they wanted to?
My point is that letting a dependent territory go on good terms is a known practice, so thanks for the examples.
Not to mention any attack coming from Earth and not from some nearby (in ship travel time terms) will be known for months if not years in advance.
I think this will drive the proper colonization of Mars.
Science, of course, but it won't require a large self-sustained colony, much like Antarctica, or oil / gas fields of Siberia, or oil rigs in the ocean.