There are two very clearly points of “control” established in Undertale:

Player Action, and Non-Player Action. Acts done through pressing buttons, and acts done without input.

When deciding who is “responsible” for genocide, you need to make a stance over which is done by Frisk and which is done by Chara.

If we wanna make the blunt statement that “Churro did the genocides”, that would establish that Player Action = Chara action... which, alongside not at all fitting with the dialogue at the end of genocide, would also require you to concede that Chara did EVERYTHING. 

They did pacifist, they did TRUE pacifist, they ate the pie in front of goatdad and brought the snowman piece to the surface- they found the QUICHE. Because, under this interpretation the player IS Chara. 

Which, honestly? Is a pretty interesting take as it would imply that Chara is undergoing the same process Flowey went through- helping everyone, SAVING everyone, but ultimately resetting because they weren’t satisfied.

But again, that is pretty clearly disproved by Chara’s genocide dialogue, and the fact that it would imply Frisk is the one doing things without input in genocide... which wouldn’t really make any sense at all.

So, no, I go with the opposite theory; Player Action is an action of Frisk’s (or, if you assert that the player is a character in the story, YOU- this leaves Frisk with absolutely zero character of their own though). In any case, YOU are the one that’s pressing buttons; anything done through YOUR input is your fault and yours alone. Ain’t got no one else to blame.

This, by extension, means that Non-Player Actions are actions of Chara. Which most people seem to accept, as they only come out in genocide- Frisk walking through Papyrus’s puzzles mid-dialogue, forcing you into a fight with Monster Kid, and killing Sans for you with the second strike.

And yeah, that’s all pretty bad; but they don’t start doing those things until YOU have established that purging the monster species is what you wanna do. Chara doesn’t do zilch until after you’ve killed their mother, outside of edgier narration.

And even then, throughout the ENTIRE ROUTE, all Chara does until the very end is speed things along. They skip puzzles that you wouldn’t have had any interest in doing anyway, they force you into fights that you would’ve started regardless, and they kill enemies you had full intentions of killing but couldn’t.

Now, personally, I make the assumption that Chara is just going with the flow that you’ve presented to them because they’re soulless and impressionable (like, if you spare ONE monster, they immediately cease this creepy shit), but even assuming this is what Chara wanted all along...

YOU’RE STILL THE ONE THAT GAVE THEM THE CHANCE.

No one was making you do anything, your keyboard is YOUR keyboard. You were not possessed by the imaginary ghost of the imaginary dead child to do the bad thing. You just DID IT, because you could. You could, so, you had to.

You are the one that covered the timeline with gasoline, despite MANY warnings over how much of a fire hazard it was. All Chara did was light the match.