When the DM introduces a monster to a new party in a new campaign for the first time are they under any obligation to stick to the monster manual (of any other creature book)?
Of course not.
There is value in following the standards, if you have players who like having the possibility to use their knowledge from previous games, but the DM can always take the ultimate responsibility of what kind of game to play so in general the DM is not under any obligation.
I've seen veteran players saying things like "I know this one, we need to handle it this way, trust me" at the sight of a specific monster. If the monster doesn't meet their expectations, they can either be intrigued or feel cheated, depending on the player's personality. If you are worried you have someone like that in your group, it costs nothing to warn them before it happens. As an example, I've grown a bit tired with color-coded dragons, and I would prefer to have more unique dragon individuals, so a red dragon wouldn't necessarily imply they breath fire; if I start featuring non-standard dragons in a campaign, I might just tell the players that in this fantasy world every dragon is unique. If I knew my players enjoyed surprises (and surprise
challenges specifically), I might instead have some standard red dragons first, and then one exception to screw them up. If I knew they instead valued traditionally established cliches as a way to make the game feel more predictable or comfortable, I'd go with standard monsters only. That said, adding class levels on base humanoid creatures is a fairly established tradition as well.