Given that they do maintain a masquerade (Part I), tightly or loosely (Part II), and they have a reason to maintain the masquerade (Part III) and it's not that some unknown force imposes it -- who are they anyway?
Frequently enough in urban fantasy, it's done by the mundane governments, which is logical enough in terms of control.
On the other hand, while their motives in acting could vary, their purpose must remain steadfast. Very little wavering, and still less change in direction, would burst the masquerade wide-open.
When I first pondered this, I thought that a democracy, where the elected officials were ignorant of the masquerade before their election, and elected by those likewise ignorant, would be a real problem. What happens when an official's first reaction is to call a press conference?
Then it occurred to me that a monarchy would have as much of a problem. Hereditary rule guarantees that at some point you will have a monarch who objects.
Then what?
If the bureaucrats are willing to blot out his memory, or give him a heart attack on the spot to silence him, why did they bother to tell him in the first place? Obfuscate their duties to their superiors the way they do everything else. They are in the business of hiding things with whatever is necessary.
These issues tend to be -- elided in urban fantasy. The mundane government that appears on stage tends to be bureaucrats protected by their bureaucracy, and with an unnatural tendency to be dedicated to their work rather than their job security. Elected officials, if they appear, tend to be unnaturally cooperative in keeping it secret without any explicit mechanisms to control them. Or they do indeed get baffled by the bureaucrats.
Then, governments do not last forever. What happens when the government changes? Part of a kingdom revolts against its king, breaks off to choose a new king for its new kingdom, and drive out all the newly foreign bureaucrats. A country throws out its king and his ministers and becomes a republic. A colony drives out its former colonizers, and then slaughters a large percentage of the bureaucrats as collaborators; it may even devolve into an anarchy. At what point does the new government take over, and how smoothly can this possibly be? Does the original colonial government have to see to that the news from this country is hushed up? How do such transitions keep the masquerade running smoothly?
On the other hand, their governmental positions may be a front for the truth. They actually answer to a conspiracy that keeps the masquerade going.
Conspiracies tend to be more logical in that they rigidly exclude anyone who will not do the right thing by their rules. If they are "in" the government, they are bureaucrats who purposely obfuscate their true purpose.
These do tend to be wizards, but often they hide only their powers, not themselves. (L. Jagi Lamplighter's Prospero's Children handles this superbly; the motives essay has more.)
Then, of course, if your world-building allows mundanes to become magical by studying wizardry, your wizards have reasons to keep them in ignorance -- in just fear of what new wizards might do, through to proud insistence on keeping their power and position.
Wizards who are themselves partly hidden point to the other side of this issue. It does not have to be mundanes who maintain the masquerade. Those who are fully hidden by the masquerade can be the master minds.
On the magical side, when the magical government does it, it does tend to be more logical in that everyone involved knows the masquerade exists. The king can choose those who support the mission as enforcers -- though the details of maintaining the masquerade do tend to be less conspicuous in such stories.
Or there's an official government bureaucracy on the magical side. Perhaps they use magic to ensure they recruit the right people. (As in Harry Potter.)
Then there are indeed works in which all the magical beings work on the masquerade, more or less. These are not so much organized conspiracies as everyone pitching in as expected. Those tend to be the works where the threat to the masquerade is not heavy, and indeed, it stays in the background as a plot device.
Which is too much to discuss in the tail end of an essay. These are the actors that works use, and more discussion of the masquerade will follow.
In Harmon's Regency Mage series, there are various "Regional Magic Guilds" that enforce the Masquerade no matter who rules the "country".
The problem for me was, "why didn't the British/English Guild" takes sides in the various English wars about who is the rightful king".
In story, the answer is "We had a higher calling", but I find that hard to buy into. (Note, apparently their only concern about telling Cromwell was "he isn't a king" but they finally had to talk with him).