No, it's not true.  Union workers cross picket lines all the time.  They're called scabs.  Some unions might force you to pay a penalty if you're a union member but if you're not in the union, then there's nothing they can do.  Kroger isn't going to fire anyone who wants to work during a strike because they don't have enough non-union employees to run all the stores in any given division.  I personally would not cross a picket line but I wouldn't walk the picket line either.  It would be like an unpaid vacation.