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I would not expect any FTL Starship to suffer from the effects of relativity (time dilation) during its service not ordinarily anyway.
Jump, warp or whatever drives "go around" the light speed limit. A starship would approach a jump point at 1g or whatever velocity, then use its jump engines. It would exit at the end of its jump at the same velocity. Momentum does not change and speed thus is relative at either end of the jump.
Even if a starship needed to accelerate at high speed for periods of time, relativity (time dilation) would normally not be an issue.
A lot of SF writers whose books involve star spanning empires use a "earth standard" for time, etc. Seems to work.
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