Lines around texture seems aren't usually caused by anti aliasing, since that's only doing multiple passes per fragment. If it isn't visible without anti aliasing, it won't be visible after either.
Texture problems are instead usually caused by mipmapping. It can make the seams a lot more imprecise.
// assume "sprite" is your Sprite object
var croppedTexture = new Texture2D( (int)sprite.rect.width, (int)sprite.rect.height );
var pixels = sprite.texture.GetPixels( (int)sprite.textureRect.x,