Anyone trying to ride on an Amerijet ID is either on their way to or from crossing a picket line; is a scab in the strict and correct definition of the term. I will do everything in my power to prevent the picket line from being crossed.
During our strike preparations we were informed that every pilot needed to walk the picket line (or do other strike work) a certain number of hours per week in order to get their ALPA strike check. That meant that pilots who commute needed to jumpseat to get to the strike center (since the company would have turned off our non-rev benefits).
It seems that a policy like yours would prevent many striking pilots from walking the picket line.