They need to be willing, but it doesn't say they get a choice or have preference for what they reincarnate as, or even if they know its reincarnate vs revivify or another spell
"You touch a dead humanoid or a piece of a dead humanoid. Provided that the creature has been dead no longer than 10 days, the spell forms a new adult body for it and then calls the soul to enter that body. If the target's soul isn't free or willing to do so, the spell fails.
The magic fashions a new body for the creature to inhabit, which likely causes the creature's race to change. The GM rolls a d100 and consults the following table to determine what form the creature takes when restored to life, or the GM chooses a form."
No, in an exception based system like D&D, specific trumps general. There is a general rule in the DMG that states that you can’t bring someone back to life against their will; and since Revivify doesn’t specifically state that it is an exception to this rule, it isn’t.
Sure you can. Reincarnate specifies a willing soul, Revivify doesnt. Meaning you could revivify against their will. A costy tool but useful one for a torturer.
Dungeon Master's Guide p.24, Bringing Back the Dead:
A soul can't be returned to life if it doesn't wish to be. A soul knows the name, alignment, and patron deity (if any) of the character attempting to revive it and might refuse to return on that basis.
That's the general rule for anything that brings the dead back to life. The spell needs to explicitly override this for it to work differently.
Reincarnate doesn't specify that the subject knows what form they're coming back to, or that "reincarnate" is being used at all. So the subject doesn't know that.
So tell me. Why specify it in Reincarnate and not in Revivify then ?
I also checked True resurection and it also specifies that the souls needs to be willing.
The answer is this : WotC fucked up.
But I agree, the DMG does says this. Buuuuut. Since some spells mentions willing souls and Revivify dont, I would say that this spell is so fast that the soul cannot decide since its probably still hanging around and so you could use it AT MY TABLE as a way to bring back a soul, willing or not.
But RAW you are correct. Still gonna use it my way as long as everyone agrees at the table. Its not like its gonna break the game.