csar: Yes your RLC circuit connected to the terminated coax cable does indeed change the termination impedance. It will do so to the extent that the RLC impedance approaches 50 Ohms near the resonant frequency. If your cable is shorter than about 2m then you may not notice anything besides a frequency-dependent load on the cable. If it is significantly longer then reflections from the load end will also make the wave-forms at both ends messier. The longer the cable, the more travel time the reflections take and the messier it gets. Chances are, your function generator is source-terminated in 50 Ohms so reflections shouldn't happen there as well.
In order to fix this, your circuit at the load end needs to do one of two things:
a - present 50 Ohms at all frequencies so you can remove the 50 Ohm resistor, or
b - keep the 50 Ohm resistor as terminator and buffer the received signal with an active (powered) circuit. Then you can build whatever you want downstream of the buffer to deal with the signal.