SRT is talking about one observer and one light clock only (and is silent about two observers and two light clocks). On the other hand, SRT is talking that in every inertial frame, physical phenomenon is the same.
There are two passenger cars. Each of these loads an observer, a light clock, and an atomic clock. Both are moving in a shuttle motion (exact opposite ; when one moves to the east, the other moves to the west). Motion of the both will be symmetrical.
《P.S.》 There are many space ships. These are moving in the Brawnian motion like. Time dilation seems to be unimaginable.