AN A320 FLT CREW INADVERTENTLY HAVE A COLLISION WITH THE R WING DURING TAXI.

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WE WERE PUSHED BACK FROM THE GATE AND HAD DELAYED ENG START DUE TO POSSIBLE SICK PAX PROB. TUG STAYED HOOKED UP UNTIL THIS WAS RESOLVED. MEANWHILE; THE AIRBUS FROM ADJACENT GATE Y WAS BEING PUSHED BACK IN CLOSE PROX TO OUR ACFT DUE TO THE PUSH LINE BEING ANGLED TOWARD OURS. THIS CONCERN WAS RELAYED TO THE GND CREW. TWO PEOPLE FROM THE OTHER PUSH CREW RAN OUT TO GET A BETTER VIEW OF THE PROX. WE WERE REPOSITIONED SLIGHTLY. WE STARTED ENGS AND RELEASED OUR PUSH CREW; WHICH GAVE US A SIGNAL THAT WE WERE CLR TO TAXI. A PERSON FROM THE OTHER CREW GAVE US A CLR SIGNAL. THE FO LOOKED AT THE WINGTIP AND BELIEVED THEM TO HAVE ADEQUATE CLRNC. WE TAXIED A SHORT DISTANCE AND THE WINGTIPS COLLIDED. THE PRINCIPAL CAUSE OF THIS INCIDENT WAS POORLY TRAINED GND CREWS. THE OTHER ACFT SHOULD NOT HAVE PUSHED UNTIL WE WERE CLR; AND THE GND CREWS EVIDENTLY ARE UNABLE TO JUDGE ADEQUATE CLRNC BTWN ACFT. THESE PARTICULAR GATES SHOULD NOT HAVE ACFT PUSHING SIMULTANEOUSLY DUE TO THE ODD GEOMETRY. SUPPLEMENTAL INFO FROM ACN 609893: A WINGMAN FROM OTHER CREW HOLDING UP WAND WITH OTHER ARM OUT HORIZLY INDICATING CLRNC; I FELT IT WAS CLR. EMER CREWS SHOWED UP. WE HAD PARAMEDICS MEET AND REMOVE SICK PAX. BAD PUSHBACK BY BOTH GND CREWS GIVING A SALUTE AND RELEASE FROM GUIDANCE WHEN IT WAS STILL NEEDED; GIVING A CLR SIGNAL AND LEAVING WHEN PLANE STARTED MOVING. RAMP SHOULD NOT ALLOW GATE X AND Y TO PUSH AT SAME TIME. PRIMARY CAUSE -- POORLY TRAINED PUSH CREWS GIVING INCORRECT INFO.