The Star-K brings three opinions about the halachic dateline:
- 90 degrees east of Jerusalem, about 125.2 E (Chazon Ish)
- The middle of the Pacific, near the international dateline (Bnai Tzion and others)
- 180 degrees from Jerusalem, about 144.8 W (Rav Tukatzinsky)
Tahiti is located at 149.4 W. Thus, the Chazon Ish and the "Mid-Pacific Poskim" hold that the those in Tahiti should keep Shabbos on Saturday, while Rav Tukatzinsky holds that they should keep it on Friday.
Rav Moshe Heinemann rules that in practice, one should observe the Biblical prohibitions on both Friday and Saturday, and the Rabbinic prohibitions only on Saturday, since the majority hold that Saturday is the true Shabbos here.
However, Chabad brings yet another opinion:
- Rav Menachem Kasher holds that there is no fixed halachic dateline, and one should follow the local community.
In practice, Chabad in Hawaii (which is approximately due north of Tahiti, so should have the same Halacha) keeps Shabbos only on the local Saturday, as can be seen here.
In conclusion, the general recommendation is to consult your local rabbi.