The sources found do not answer the question as asked. They are shown as the nearest passages located, not as a source for the claim.
The sources assembled here mostly set out the classic halachic background to Yom Tov Sheini rather than directly comparing the positions of the Lubavitcher Rebbe, Rav Ovadia Yosef, and Rav Moshe Feinstein on a visitor's status in Israel. Gray Matter I, Laws of Holidays frames the dispute as whether Yom Tov Sheini follows the general rule that a traveler intending to return keeps his place of origin's stringencies, and notes that most authorities, including a view attributed to Rav Moshe Feinstein's Igrot Moshe, hold that a Diaspora visitor must keep two days even in Israel.
The underlying reason for the second day is explained by Kitzur Shulchan Arukh Yalkut Yosef (Orach Chaim 496:1) and Mishnah Berurah (496:1): Chazal retained the second day out of concern that troubles and dispersions might cause the Diaspora to forget the calculation of the calendar, even though the fixed calendar is now reliable, and Chayyei Adam (Shabbat and Festivals 103:1) adds that Eretz Yisrael communities that received the court's messengers in time kept only one day.
The status of settlements in Eretz Yisrael itself is a point of dispute among the Rishonim: Mishneh Torah (Sanctification of the New Month 5:11-12) rules that places settled in the second conquest of the land follow their ancestral custom, while Shoel uMeshiv (Mahadura II 2:85) records that the Rishonim disagreed over whether all of Eretz Yisrael, even for Rosh Hashanah, requires two days, citing the Rif's position that the enactment was never uprooted there. Teshuvos V'hanhagos (4:115) addresses this directly, stating that although one view holds new settlements keep two days, the Ritva and the Teshuvot HaGeonim citing Rav Saadia Gaon hold that all of Eretz Yisrael keeps only one day, even where the messengers never arrived, and Tzitz Eliezer (3:23) likewise addresses the practice of keeping only the first day, following the view that the second-day enactment was established only for the Diaspora and not for Eretz Yisrael.
Rav Mordechai Eliyahu (Shut HaRav HaRashi 36:15) and Rav Mordechai Eliyahu (Shut HaRav HaRashi 36:13) take up a related but distinct question — how a traveler who goes abroad for a defined period, or who questions whether the original rabbinic concern for calendar confusion still applies today, should conduct himself regarding prayer and tefillin on the extra day — rather than the question of a Diaspora visitor in Israel as framed here.
Igrot Moshe (Orach Chayim 1:97) addresses a different matter, namely how the onset and end of Shabbat are determined by local sunset and the appearance of three medium stars, with added stringency in low-lying or neighboring locations, and does not bear on the Yom Tov Sheini question.
Ma'ayan Omer (vol. 3, perek 5, siman 1) likewise addresses an unrelated matter — advising that congregants recite Shehecheyanu individually on Yom Kippur if the person honored with the Torah is not observant — and does not bear on the second-day question either.
Rav Eliezer Melamed (Peninei Halakhah, Festivals 9:4) is identified only by its heading on the obligation to keep two days of Yom Tov Sheini and where that obligation applies, without further passage content surfaced here.
Shemot 23:19, concerning bringing first fruits and the prohibition of cooking a kid in its mother's milk, does not bear on the question of Yom Tov Sheini in Israel at all.
