During the times of false messiah Shabbetai Tzvi, and for several decades afterwards, many well established rabbanim [1] believed him to be Moshiach. Some even maintained this belief after his conversion to Islam. May one learn from the seforim of those who maintained such belief?
[1] see Bezalel Naor's Post Sabbatian Sabbatianism for a recent survey of the academic literature on this topic
It would appear based on the article Reb Shlomo and Tu Beshevat (scroll to the bottom) that the sefer Hemdat HaYamim, which clearly contains sabbatean material has been accepted.
for those following Lithuanian tradition, both the Gra and Haayim of Volozhin accepted Hemdat Yamim.
So I would surmise that as long as no sabbatean theology is espoused works of this nature should be permissible to study (obviously this is not a psak, just speculation).
Pinchas Giller (in Shalom Shar'abi and the Kabbalists of Beit El) quotes Rabbi Yaakov Moshe Hillel as expressing permission to learn a Sabbatean book, Sha'ar Gan Eden. There is some controversy as to the Sabbatean nature of the work but this article argues that it is clearly a Sabbatean work. Giller states that R' Hillel allowed one to learn
the Sabbatean work Sha'arei Gan Eden by Jacob Koppel Lifscheutz...For Hillel, the odd inclusion of occasional Sabbatean materials...is less of a problem than the appearance of Sarugian materials." p.103
