Straight of Grain

I'm cutting up an old wool skirt into a 1940s skirt. Right now the layout is giving me fits, even with piecing to give a yoke effect on the front pieces.  The original skirt is a two-gore flare, cut on the bias. It would make life a lot simpler if I didn't have to lay all the pieces out exactly on the straight of grain. What horrible things would happen if it wasn't precisely on?  The fabric is a wool blend, fairly sturdy and tweedy.