Unlike the Christian church, Hebrew Israelites are not centralized, so the beliefs totally vary from person to person.
For me as an Israelite, I believe in the Old AND New testament. In the OT, we were commanded to follow and observe the holy days forever. And in Jer. 10:1-3, we were commanded to not observe Christmas and other pagan holidays.
Since I do believe in the NT, I acknowledge that Yahshua was the perfect sacrifice for our sins, and sacrificial law was set aside until his return. But there are many Israelites that only believe in Torah, some only full OT itself, and some, the whole bible. It just varies.