I don't "think" the OP is contemplating crossing a picket line.
I do not mean this in any derogatory manner, but it is possible the OP is new to the airline world and just wants to know what the heck happens to him or her if 357 strikes, I would have the same concerns as a new hire.
I, as opposed to some F9er's, believe that 357 would protect their new hire pilots. 357's new hired don't correlate in any way to 357 and F9 pilot's relationship.
Honest question, do the RAH new hires begin paying union dues on the day they enter training at RAH? Are they considered union members as of that date? Or do they not pay dues until they are off probation, if you have a probationary period?