Don't worry about the straight of grain and cut the fabric so it is straight for your use. I would starch it well first to help control the slight bias edge you will have. Then handle the fabric with a gentle hand. Hope this will help.
cool star fabric!
peace :D
Okay. if the star design is going to be cut into small pieces or HST (half square trianlges) then cut it on the straight of grain. It won't matter if you lose the star.
For future reference if you want to use a stripe or pattern that needs to be cut on a line to match, like a plaid, you will cut following the pattern and not the SOG (straight of grain). I would always starch the fabric before cutting.
HTH (hope this helps)