The combat rules state, on page 189 PHB:
Initiative determines the order of turns during combat. When combat starts, every participant makes a Dexterity check to determine their place in the initiative order.
Can a character opt to not participate in combat? That is, they do not roll initiative, they just huddle down and remain passive? So I can rule that they don't control any space in combat, in order to free up that space for the creatures that are acting in combat. (The noncombatants could obviously still be attacked, but would not have movement or actions like reactions, no Dodge actions, not be subject to the suddenly extended space requirements that active combatants need etc).
For example, the PCs escort a group of refugees down a narrow corridor and are ambushed by orcs. Can the refugees stay out of the fray and allow the PCs to move through or fight in the space they would otherwise take up (especially if everyone was walking much more closely than the wide spacing of combat)?
The question is not limited to NPCs.
Background
I think the underlying problem I have is that switching from narrative to combat mode changes the space requirements of a creature from how much space it physically needs to a suddenly much larger area, which in combination with the requirement that no two creatures may share a space, leads to various problematic outcomes. Like the one described above with the refugees, or like this one, where creatures would have to jump of a carpet of flying, just because someone attacks them, which is the question that caused me to ask this one – but there are many others conceivable. I am trying to understand if characters opting to not participate in combat could be one tool to address this rules artifact.
Best Answer
The DM controls the encounter
As the DM, it is your job to create the encounter and set the stage for the story you're telling with your players. If having NPCs not participate in the encounter makes sense for the encounter, then set the stage with them not participating.
I just ran an encounter where the PCs had to attempt a hostage rescue. I had the hostages on the map, but I didn't put them in the initiative tracker. They were still obstacles to move around and deal with on the map, but they didn't actively participate (other than being targets for the NPCs and provide another task, to rescue them, for the PCs).
Whether or not you have NPCs join initiative and combat itself is really just one of the tools you have in your storytelling toolbox.
Play the game
As for PCs, if a player doesn't want to participate, then that's kind of on them. Their absence will likely make the encounter much more deadly for their companions and they'll end up just sitting around the table while everyone else plays. To each their own? Or not, if you don't want someone not playing at the table.
However, if a player is asking to not participate in order to achieve a mechanical advantage or change how the game is played, then as a DM I'd be highly unlikely to allow that. That's playing a different type of game.