LGT ON ILS TO SIDESTEP TO PARALLEL RWY RECEIVES TCASII RA AS SECOND ACFT PASSES ON APCH.

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ATIS RPTING CLR AND 20. HOWEVER; LNDG INTO A BRIGHT SETTING SUN AT XXPM PM LCL TIME; RWY WAS VISIBLE ONLY ABOUT 3 MI OUT. WE HAD BEEN CLRED ON AN ILS TO 25L; SIDESTEP AND LAND 25R. APCH CTL DID ADVISE US THAT A FLT WAS BEHIND US; HAD US IN SIGHT; AND WOULD LAND 25L. WE WERE STILL ON THE ILS APCH; (ATC NEVER CLRED US FOR A VISUAL) AND HAD SIDESTEPPED TO 25R WHEN TCASII GAVE US AN RA 'MONITOR VERT SPD' AND SHOWED PICTORIALLY FOR US NOT TO SHALLOW OUR DSCNT RTE. THIS WAS CONFUSING AS THE FLT BEHIND US HAD BEEN BELOW US. LOOKING OUT THE L WINDOW I WAS STARTLED TO SEE THE TFC THAT HAD BEEN BEHIND US ABOVE AND TO OUR L; NOT MORE THAN 600 FT AWAY. WE WERE TECHNICALLY STILL ON AN ILS TO 25L AND ANOTHER FLT ON APCH TO THE SAME RWY WAS PASSING US! WATCHING HIM TO BE SURE OF HIS PATH; OUR OWN APCH DESTABILIZED; I.E.; AIRSPD AND DSCNT RATE BOTH INCREASING. BUT A GAR WAS NOT AN OPTION. TCASII WAS YELLING AT US TO NOT SHALLOW OUR DSCNT; WE COULDN'T TURN L WITH THE TFC JUST MENTIONED; AND THERE WERE APCHS BEING CONDUCTED TO RWY 24. THE GAR DOOR HAD BEEN CLOSED. THIS IS A DANGEROUS SIT. UPON LNDG; I CALLED THE TWR AND TALKED WITH THE SHIFT SUPVR WHOSE REPLY WAS THE ATIS SAYS WE'RE CONDUCTING PARALLEL VISUALS; SO YOU ARE ON YOUR OWN! EVEN THOUGH I WAS NOT ON A VISUAL! IT SEEMS THAT THE ACCEPTANCE RATE OF THE ARPT WOULDN'T BE LESSENED IF TFC WERE STAGGERED SO AS NOT TO FLY WINGTIP TO WINGTIP; AND THAT TFC NOT BE PERMITTED TO PASS; ESPECIALLY WHEN RWYS ARE ONLY 750 FT APART. IF THE TWR HAD ONLY INFORMED US OF THE TFC AND TOLD US THAT WE WERE BEING PASSED IT WOULD HAVE BEEN A TREMENDOUS HELP. SUPPLEMENTAL INFO FROM ACN 268985: TWR CTL WAS CONTACTED OVER LIMMA OM AND ASKED US IF 25R WAS IN SIGHT. WE RESPONDED NEGATIVE AND WERE TOLD TO RPT IT WHEN IN SIGHT. AT APPROX 3 NM TWR CLRED US TO LAND 25R; THE RWY WAS JUST VISIBLE AND WE MANEUVERED TO LAND RWY 25R. APCH CTL CALLED OUT TFC AT 6 O'CLOCK THAT HAD US VISUALLY WHEN INITIAL CLRNC FOR APCH WAS GIVEN. AT APPROX THE OM A TA APPEARED AT 6 O'CLOCK AND CONTINUED UNTIL SHORTLY AFTER CLRNC WAS GIVEN TO LAND 25R (FOR US). AT THAT TIME THE TARGET BECAME AN RA WITH MONITOR VERT SPD COMMANDS WHILE THE ACFT PROCEEDED TO OVERTAKE US AND LAND 25L. VISUALS AS WELL AS ILS WERE ALSO BEING CONDUCTED TO RWY 24. THERE WAS NO SAFE WAY AVAILABLE TO BE ABLE TO EXECUTE A GAR.