Let's say the Mars One project, regardless of its problems with feasibility and practicality, does push through. Say, in 2024, Filipinos along with other nationalities are able to live in Mars and "colonize" a certain area.
How will the Filipino cultural sensibilities be applied to their new home?
What would they bring to their new “colony”, so to speak?
How would Filipino culture be affected by space exploration? (I could imagine, they won't be able to cook adobo anymore, for instance. They'd also be dealing with a different kind of weather, no longer the tropical one we have in the Philippines. Plus, they'd be living with a much smaller group of people from different nations.)
And my long-ish answer:
Kim Stanley Robinson addressed this issue in his Mars trilogy. Essentially, he was saying that when you colonize a new planet, you have to obliterate your old cultures in order to build a new one.
Let's look at what culture is. "Culture" as we use the term is a concept of recent invention. It's a set of conventions adopted by a group of people and typically expressed as commonly understood symbols. Culture is a tool to pass on knowledge, customs, taboos, etc. to members of that community.
Now apply that to the Mars One project. According to their plans, they'll be sending their volunteers in batches of four people per trip. Assuming one landing every eight earth months, in two earth years you'll have only twelve people on the planet. Presumably, it will be an international crew, therefore coming from different cultures.
Mind you, those people will be stuck there for the rest of their lives. Is there any good reason for the colonists to hold on to the conventions of their past, conventions that might, for instance, lead to misunderstanding and conflict? They might call up old memories on those lonely nights when they're feeling nostalgic and regretful, but other than that, they'll will serve no purpose in their new environment.
Consider this thought experiment. What happens if you put together a Filipino, a Nigerian, a Chinese, a Tibetan, an Indian, a Pakistani, a Frenchman, a German, and an American on a project, isolate them from the rest of the world for an extended period. If they're going to survive, they'll have to let go of their old cultures and develop a new one.
"Ah," you say, "but what if we send a GROUP of Filipinos as colonists?" And my answer to that would be: what for? What arrogance could make us think that Filipinos are THAT special as to deserve their own space and their own contingent on a new planet? And furthermore, which "Filipinos" do you mean? Manilenos? Boholanos? Cebuanos? Tausug? Blaan? How do you think that will play out? We're not nearly as culturally united as you think.
Now, if you really want to put absolute primacy on "culture" to the extent that you want to impose it on yourself and on others in a new colony, then my advice is: don't leave home.
Here's some homework for you: you frequently refer to adobo as the signifier for Philippine culture. Is it really the same across the entire country? Or are they really different dishes with commonality in one or two ingredients? What environmental necessity prompted the development of adobo?