For hand pieced seams, you always want to press to the side because that makes the seam stronger. Seam strength is not an issue with machine piecing. The quilters who gasped at seams pressed open did not understand this difference.
As mentioned, seams pressed open can allow batting to beard through the seam. However, this is usually an issue only when doing stitch-in-the-ditch, especially if the batting is polyester and/or the stitch length is not small. Shortening the stitch length (and having a balanced machine stitch; some machines are really poor at balancing the top and bottom threads) can prevent this problem, plus cotton battings are highly unlikely to beard in this manner.
Pressing seams to the side can speed up piecing of certain types of pattern that involve lots of seam matching -- for example, quilts made of 9-patch blocks.
Pressing seams open can help when matching strip sets in patterns made exclusively of strip sets.