Also check your hand position to make sure your fingers are coming in straight to the strings and not angling where they can accidentally touch other strings.
I'll try to explain this in words as best I can. Make your C chord and make sure your thumb is in the center of the back of the neck, probably just above the first fret. Now - push your left wrist slightly forward and watch what a difference that makes in the angle of your fingers coming down, especially the index and second fingers. From the first knuckle to the tip, that section of the finger should be almost a perfect 90 degree angle.
When someone showed me that simple change, it really made a difference in my playing, as it almost completely eliminated my accidental mutes.
"This old guitar gave me my lovely lady.
It opened up her eyes and ears to me..."