Anyone is free to travel anywhere, as long as they don't trespass on another's property rights, but this principle does not mean that the undertaking the journey is wise and worth the resources used in it, or indeed, whether the undertaking is a good use of time. These considerations are especially significant if the journey is very expensive and/or if it is dangerous to life. If the latter consideration is the case, we must ask whether the risk is worthwhile.
Now, space travel inherently dangerous because it involves humans operating in the most hostile of environments, using technology sometimes, nay oft-times, at its limit and working in an environment for which humans have not evolved to cope, for we evolved to dwell in the protective ambience of a wonderful planet, Earth.
So is leaving Earth wise? Well, we send sophisticated robots to the planets, and there is no harm in this, and we have visited the moon, though, let's consider this cautionary, no one seems urgent to return, there being no pressing economic and/or political or social need to send a manned crew there. But is there need to send crewed ships deep into space? It seems ironic that while society is busy replacing workers with robots we are considering sending a human-crewed craft into an area where robots have already done a good job.
So what is the purpose of space travel? Science for science's sake? A good idea, but does it justify massive resources that could be used more beneficially elsewhere, and how much risk to human life can be justified in the cause of science? Science should benefit all humans, and so the gains from scientific progress must be weighed against losses to humans. The advance of science should not unnecessarily risk human life. Undertaking space flight is a great adventure, but humankind's great adventures of exploration always had a serious purpose. The adventure was a side effect of a journey of scientific discovery or economic enterprise.
There must therefore be an economic and/or social purpose for space travel commensurate with the risks and sacrifices that it involves. Finding a new home for humankind is not such a purpose, as only a tiny minority of humans could inhabit Mars, which is the only vaguely inhabitable planet other than Earth. Earth is our home and it is up to us to make the most of it, not ruin it then find somewhere else to ruin.