Does one cancel the other out? They both say “immediately” on defeat but Chant requires a save. They also both specify setting up in the defeated character’s square. How does this play?

The rules committee is going to discuss this. My first impression was that this interaction involves characters and abilities from multiple players, who both have the ability to bring in a new character simultaneously; the effects are not really applying to one player's character because adding the zombie doesn't affect the character that was defeated. So the acting player (the one who defeated the Nightsister) would go first. I would also assume based on other past rulings that whoever went second would still get to add their character, it would just set up in the nearest legal square instead.

Neither Chant of Resurrection nor Rakghoul Disease "turns" one character into another, strictly speaking. Both of them say that when a specific character is defeated, and is removed from the board, you get to add a different, new character to your squad in the square formerly occupied by the defeated character. (It is true that Rakghoul Disease does affect the original character in that it deals an extra +10 damage which can be avoided with a save of 11. But the other part of Rakghoul Disease does not affect the original character before or after it is defeated.) As for Chant of Resurrection, it seems like the character rolling the save would be Old Daka (or Merrin) based on how the ability is worded. A defeated character doesn't typically roll saves.

I'm not aware of a single ability that adds a character to your squad where you wouldn't get to add them because the specified square(s) is taken. Immediate Reserves works like this if all the adjacent squares are occupied (though this is not written specifically into the text of the ability). With some abilities, like Placed Order, it is in the glossary. Frozen in Carbonite, Force Essence, and so forth, the consistent ruling is "Place it as near as possible."

To be clear, the above is not a ruling. There just doesn't seem to be anything in the text of Chant of Resurrection to indicate that the defeated Nightsister makes the save. Defeated characters don't act in that way as far as I'm aware. ("Zombie" CEs and Avoid Defeat etc are a little different because they are resolved before the character is removed/defeated.)

There's plenty to indicate that the defeated Nightsister is intended to make the save roll.
Old Daka's Witches' Orb SA says Nightsisters cannot be prevented from spending Force points to reroll Chant of Resurrection saves.

The Chant of Resurrection text should indeed be more clear that it's the defeated Nightsister making the save.
However, anyone who has played against Deathshots has seen defeated characters acting like this plenty.
You are defeated before you leave the map.

RotS 14 Mon Mothma
Commander Effect
Followers within 6 squares can make 1 immediate attack at +10 Damage when they are defeated.

JFO 5 Merrin, Nightsister of Dathomir & CaR 34 Old Daka
Chant of Resurrection (Force 2, replaces turn: For the rest of the skirmish, whenever a living Nightsister ally is defeated, with a save of 11, you can immediately add a non-living Nightsister to your squad)

While I think the defeat of 1 character resulting in the addition of 2 new characters is asinine.
The rules committee can do whatever they feel appropriate with the Rakghouls vs Chant of Resurrection interaction.
I'm more concerned with Chant of Ressurection, Witches' Orb, and Old Daka's CE working as intended.

Makes sense. Hopefully, a glossary addition could clear up who makes the Chant save.

The Rakghoul vs Nightsister thing is a weird interaction I wouldn't expect to see often.
Best of luck to our Rules Committee as they attempt to untangle that mess.

Sounds good