NON ADHERENCE TO ATC CLRNC ACR X TCASII RA HAD CONFLICT WITH ACR EVASIVE ACTION TAKEN.

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THE OTHER ACFT DID NOT MAINTAIN VISUAL SEPARATION AS IT WAS INSTRUCTED BY CTLR. THE CTLR DID NOT SUPERVISE HER PREVIOUS CLRNCS NOR DID SHE STOP TALKING LONG ENOUGH FOR LISTENING PURPOSES. SHE WAS OVERLOADED FOR HER CAPABILITIES. ACR X HAD BEEN PREVIOUSLY CLRED FOR AN ILS RWY 25L APCH AND SLOWED TO 15 KTS. CTLR ADVISED THAT TFC FROM THE S HAD US IN SIGHT AND WOULD FOLLOW US TO RWY 25R. I RECONFIRMED THAT WE WERE LNDG ON RWY 25L. CTLR ACKNOWLEDGED. I THEN SPOTTED THE TFC AT APPROX 10 O'CLOCK (TCASII SHOWED IT TO BE AT 6200 DSNDING). ACR Y CONTINUED CLOSING TO THE 9 O'CLOCK POS IN A SLIGHT L TURN (I DO NOT BELIEVE THAT THEY SAW US AT ALL; OR THEY WERE JUST PLAYING GAMES). THEY DISAPPEARED DIRECTLY ON TOP OF US AND DID NOT APPEAR ON THE OTHER SIDE. THEN THE TCASII TURNED RED WITH INSTRUCTIONS TO CLB AT THE MAX RATE (IT NEVER WAS YELLOW). FO STARTED TO CLB. I TOLD HIM TO STOP BECAUSE TCASII SAID TFC WAS AT 3200 FT DSNDING. WE WERE AT 2700 FT. TCASII THEN CHANGED (STILL ALL RED) AND TOLD US TO DSND AT MAX RATE. I TOLD FO TO GAR AND TO TURN L (S AWAY FROM RWY 25R). HE CALLED FOR GEAR UP ; FLAPS 20; WHICH I DID AND HE TURNED. ALL THIS TIME I WAS TRYING TO TELL CTLR WHAT WAS HAPPENING. CTLR WOULD NOT LISTEN. FINALLY; TCASII RETURNED TO NORMAL. FO SAW GLIMPSE OF ACR Y OVER R SIDE 3 O'CLOCK AS WE TURNED L. TCASII WAS CORRECT. A DIFFERENT CTLR CAME ON RADIO AND ASKED WHAT WAS HAPPENING. I ADVISED THAT WE HAD HAD A CONFLICT ALERT. HE ASKED IF WE COULD STILL LAND. FO SAID HE COULD; SO WE DID. ON GND I TALKED TO THE APCH CTL SUPVR. WE HAD DISCUSSION AS TO WHY I HAD TURNED L RATHER THAN HIT THE OTHER ACFT. HE SAID PARALLEL APCHS WERE APPROVED. I SAID YES BUT WITH IN TRAIL SEPARATION I TOLD HIM WHAT I THOUGHT OF HIS APCH CTL.