I would reterminate that end to BNC. If you were to use an RCA-to-BNC adapter, the adapter itself would undoubtedly introduce a significant impedance discontinuity. And the RCA plug would also, unless it is one of those that is specifically designed to have a 75 ohm characteristic impedance, such as some of the Canare's.
BNC's are specifically designed to have accurate characteristic impedance
, and will have good performance at the high frequencies that are present in digital signals.
Also, the fact that the other end is RCA will not nullify a lot of the benefit of having a good impedance match at the BNC end. Having a good impedance match at one end will minimize the number of times that waveform reflections resulting from impedance discontinuities re-reflect back and forth from one end of the cable to the other, before decaying to insignificance.