Loricism's primary focus is in leading the individual closer to self-mastery, which includes self-awareness, self-confidence, self-control, etc. In developing the self, it is only natural that a sense of ownership over one's life emerges, as does a sense of autonomy. One ultimately moves away from the need for social validation; one no longer seeks out happiness or content in the perception or behavior of others; one no longer blames external sources, other people included, for problems.
In discovering this ownership of self, it follows that one also sees that this applies to others as well (the 11th Key, Consider Other Masters). In essence, if we develop the wherewithal and self-respect enough to assume ownership of our own lives, and we set and enforce boundaries to prevent others from hijacking control, it is only reasonable that we do the same for others.
This concept, combined with the ability to let go of things that are beyond our control or don't infringe on our own ability to live our own lives (caring too much what others are doing with their own lives) leads to a "live and let live" mentality.
Essentially: do as you will, so long as you aren't inflicting unreasonable suffering upon others.
But what is unreasonable suffering? To understand this, we must first account for what suffering is. For our purposes, we define it as "pain, misery, or distress." We try to avoid inflicting these things onto others. So what exactly does "unreasonable suffering" mean, then?
Sometimes, some people may suffer in response to a decision we make, despite our best efforts to avoid such a thing. It is our duty to attempt, to the best of our ability, to limit the amount of suffering we cause. (See the infamous Trolley Problem thought experiment.)
Through careful consideration we attempt to reach reasonable conclusions. This type of suffering might be considered reasonable, even if it is still undesirable. Unreasonable suffering, then, would be anything out of malice, self-interest, unethical, etc.
Thus, Loricism's approach to social issues is to allow other people to be their own Masters, unless they are inflicting unreasonable suffering onto others. If they are not causing suffering, why do we care what they do? To be too concerned over what others are doing is counter to the 8th Key (Be Vigilant, Be Diligent) and the 9th Key (Focus Within). And of course there's also the 11th Key we mentioned earlier.
The 8th Key teaches us to focus on what's important and get rid of things that cause us self-inflicted stress or anxiety. Being overly concerned with everyone else is one way we inflict undue stress on ourselves. Similarly, the 9th Key teaches us to focus within, on what we need to improve in ourselves first. Given that 3 out of 11 Keys here run counter to getting in everyone else's business, it is clear what Loricism's stance on social issues is. Give everyone the freedom to live their lives however they want, so long as they're not hurting anyone. Freedom is a valuable thing, right? So why shouldn't we allow others the same freedoms we want for ourselves?