On the site Why Linux is better there is an article about backdoors in proprietary software. The author writes that because the source code of proprietary software is secret:
The problem is they [the programmer, ed.] can put whatever they want in their recipe, without us knowing.
Subsequently he a gives an example what happened to some Chinese users of illegal Windows copies: black screens every hour. Though in this case this might be a legitimate action by Microsoft to enforce its copyright, nastier things could happen.
In fact proprietary software is a potential threat to national security because of these backdoors. Those might allow foreign powers, think for instance about the NSA, to spy upon governments or even worse.
Open source software could contain backdoors, but because the source code is public, they could be easily spotted. Hence by using open source software, space settlements could improve their national security.
In addition open source software allows better detection of bugs (unintentional flaws) which could be used by cyber criminals (so-called zero days). With proprietary software such zero days could remain for years without detection and if detected one is dependent upon the supplier for a fix. However, open source allows users to fix bugs themselves (or to hire someone to do this).
Possibly governments should implement a reward scheme. Anyone who detects and subsequently report a bug or backdoor will receive some money. This will significantly increase national security.