First, why space colonization is important? Staying on Earth is nice, however the time is ticking. Sooner of later there will be a natural of "human provoked" event that will destroy the human civilization on Earth. A big enough meteor will likely strike Earth way sooner that the Sun will deplete. Remember the dinosaurs? It would be good to know that all we care about in this life will have a chance to survive, even on another planet.
You might think that deriving morality from this is too far fetched, but let's take some examples. Of course, as long as there is not even an uniform understanding between religions about morality and there are also conflicts with the secular morality, we cannot have a perfect match. However, the "space colonization" approach might give answers very close to the mainstream convictions of today's people. It could also give similar answers for the moral question of ancient people!
Precepts like "do not kill" or "do not steal" or more general "do not harm" are almost universally accepted by both religions and secular moral. How does this derive from the space colonization question?
Let's imagine a society without such precepts. A society where each member should watch his back and belongings... Will this society provide the welfare that we desire? Would this society permit human organization for a big objective, like space colonization? I would say a sure "no". A prerequisite for space colonization is a certain level of welfare and surplus in society and a common set of rules that facilitate collaboration. Usually the science people are less able to physically defend themselves; in order for them to flourish, they need a society where individuals are protected from abuse.
Help the ones in need, give
Of course, our empathy makes us susceptible to help the poor and the ones in need. We also feel it's good that poor children should have the right for decent food and real opportunity for education. Actually, this is also good for society in general, on the medium and long term, because it creates more valuable citizens who can better produce goods and innovations. In the same time, this also contributes to... increasing the chance for space colonization. Latent geniality tends to be equally distributed among population. We just need to provide opportunities for many of these latent capacities to be developed, we don't know from where we will get the next Einstein.
These were a bit easy ones, because space colonization implies a certain welfare in society, so it does not add much over an utilitarian approach, based on happiness. Let's try something more complicated.
Here there is still a debate even inside the secular world (like conservative parties), but mainly this is an issue derived by religious precepts. How the "space colonization" question would answers to this question? Well, if you would ask this question hundreds and thousands of years ago, when the human population was scarce and the mortality was high, the answer would have been that human society needs as much reproduction as possible. There was a need for people to procreate and take care of the children. There were also diseases spread by sexual promiscuity. A lower tolerance for gay activities and heterosexual promiscuity have probably increased the likelihood of human flourish, increasing the chance for... space colonization :)
When we are talking about the last hundred years, things looks a lot different. We cannot imagine today's science and art without the contribution of gay members. Think about Alan Turing for example. I'm not sure if all Germans today agrees that cracking Enigma was a good thing for humanity, but his contributions on computer science are undisputed. Special gifted people tend to be more... special, and we should accept some eccentricities for the other benefits to society they might provide. This will surely make us more likely to be able to colonize the space one day.
Low carbon society
One place where "common welfare" would not give the same answer as "cosmic colonization" is the idea of small auto-sustainable social groups. This is a move that aims to a more ecological life, with less negative impact to nature. While this is a good goal if we want to live until we will be able to colonize the space, it is not the solution to long term humanity survival. We can live thousands of years in harmony with nature, without carbon emissions, without pollution. But the time will come and the "nature" will strike humanity on Earth, no matter how gentle we were with her. At that time, it would be good to have a backup location outside Earth. Unfortunately, cosmic colonization is not possible to be created in such a society that lives on a very small scale of organization. We also need to do the space expansion before we deplete the energy reserves we have. At least we should research and find another energy source before we deplete the fossil energy reserves (like oil, gas).
Each time when you have a moral matter, or any difficult decision, just try to answer to this question: "will this move humanity closer or further from space colonization?" Many times the impact is hard to estimate, but just for exercise... Does the action that seem to contribute more to space colonization correspond to your common moral sense? Does it correspond with your political, religious convictions? Tell me about your experience, please leave me a message!
P.S. Even if the answer seems very clear, use your common sense before you action! Remember: any use of my ideas to justify doing harm is misguided!