Nice idea. Although the user-base of time travellers might be a bit limited. I would suggest broadening your product to include the soon-to-be emerging high relativistic speed and FTL travel sectors. Part of the process of friending someone could be to indicate how your respective light-cones intersect, for example.

If your network is ad-supported then there might be extra complications in temporally localising the ad content so that it doesn't induce the wrong kind of causality violations. You might want to give that some thought, now or in the future.

Disclosure: I'm not a VC in this timeline.