Those are not audio 'splitters' really. Your single green connection is a stereo audio connection containing the left audio signal connection, the right audio signal connection, and a ground connection. The stereo 1/8" (3.5mm) mini connection to stereo RCA connection does not 'split' the signal connections as they are already independent wired connections. It does split the ground, which will have no impact at all on your audio quality.
So, not only is this fine, this is the proper and typical way to connect a stereo mini connector to RCA inputs. It is how you would connect your iPod or PC to any typical system with RCA inputs.