Comment from an industry outsider..
In my commercial experience (outside aviation) the best way to break down barriers is to avoid at all costs an 'us and them' situation. Unfortunatly this can be created from nothing ie - FA thinks there is a problem with FD crew because culture or gossip instils this into her. I think it is probably a larger issue outside your control flappy.. it really should be down to the company to positively encourage a 'teamwork' ethos and give the time and facility for this to happen - without either party feeling that they are being forced into anything.
What happens on stopovers - do crew mix freely, socialise together etc? It would appear not. Is there generally arrogance shown to cabin crew from the people at the front - or is it assumed by cabin crew as casual communication on the job is not as easy as in most professions?
Tim