Pets make so much noise _____ troubles residents a lot.

[嘟嘟嘟嘟]

Pets make so much noise _____ troubles residents a lot.

Is "that" or "as" right for the blank, or both?

 

[probus]

Neither is natural. "Pets make so much noise that it troubles residents a lot" is more natural, but I would say "The noise made by pets troubles ..."

 

[嘟嘟嘟嘟]

Neither is natural. "Pets make so much noise that it troubles residents a lot" is more natural, but I would say "The noise made by pets troubles ..."

Maybe they are unnatural, but are they correct in grammar?

 

[Tdol]

Instead of that, I would use a comma followed by which. You'd need more context for that to work- it doesn't work in your standalone sentence. As could work in a few British dialects, but not in standard English.