Karaite Jews observe only one day of Rosh Hashanah because they do not accept the rabbinic basis for adding a second day beyond the Written Torah.
Karaite Judaism emphasizes the Hebrew Bible, or Written Torah, rather than rabbinic oral law as the ultimate religious authority. Because the Torah describes the festival as a one-day observance and does not explicitly command a second day, Karaite communities observe the first day of the seventh month only.
This differs from mainstream Rabbinic Jewish practice, in which Rosh Hashanah is generally observed for two days, including in Israel. The additional day is linked historically to uncertainty over when the new moon was sighted and the new month officially began. Rosh Hashanah is unusual because its two-day observance is retained even where other festivals are celebrated for one day.
Karaite practice should not be confused with Reform practice. Many Reform congregations observe one day, but for different historical and denominational reasons. Sephardic, Conservative, Hasidic, and other Rabbinic Jewish communities generally follow the established two-day tradition, with variations in customs and liturgy.