Most: Poisoned (434). Least: Incapacitated (1); Unconscious (26).
As of the writing of this answer, there are 1652 total monster/NPC statblocks listed on D&D Beyond.
We can use the filtering options in D&D Beyond's monster listing to see how many monsters/NPCs across all sources are immune to each condition:
Ignoring the outlier that is the Invisible condition:
The condition that the most number of monsters listed on DDB are immune to, by far, is the Poisoned condition, with 434 listed monsters that have an immunity to it. The conditions with the next highest number of monsters immune to it are Charmed and Frightened, with 290 monsters (there's obviously overlap, but the lists aren't identical).
The condition that the fewest monsters are immune to is easily the Incapacitated condition; only the warforged colossus is directly immune to it. After that, monsters are least often immune to the Unconscious condition, with 26 monsters listed, and the Stunned condition, with 39 monsters immune to it.
Note: DDB's monster listing now lists specific variants of monster statblocks (e.g. an adventure taking an existing monster and making modifications to its traits or attacks) separately from the base statblock, though it did not do so when it first began listing monsters. As a result, these numbers might be slightly overestimating the actual number of monsters excluding such variants - but I suspect the difference won't be enough to change the relative rankings between conditions.