If you ask contemporary Rabbis the answer is yes. Why? Their point of reference is the Talmud that was intact going back to the 5th Century C.E. where the rabbis could comment on the Christian assertion that Yeshua was the promised messiah. The behavior of Byzantine and Western Christians against the Jews solidified this point of view. In the 11th Century this perspective was reinforced by the most important of rabbinical sages Moses Maimonidies. His work can be found in the back of the Talmud where it is known as the Mishneh Torah.
The Jewish people from early on are taught that the rabbis are to be followed. A literal observance of their teachings leads to rabbinical orthodoxy. Conservatism follows the rabbis in most teachings but not all. To a lesser degree are the Reform and Revisionist congregations. The Orthodox see the other Jewish congregations as less Jewish than they. The more liberal Jews see the Orthodox as narrow minded. Truth be told the Orthodox do not want their offspring marrying less observant Jews unless those Jews are willing to make a commitment to rabbinical Orthodoxy.
The central point of agreement within Judaism is that Yeshua is not the messiah. The rabbis have concluded that anyone born of a Jewish mother who rejects the messianic claims of Yeshua is Jewish. Thus anyone born of a Jewish mother who believes in Yeshua is no longer Jewish. The rabbis are correct if by Jewish they mean rabbinical Judaism for Yeshua rejected the tradition of the elders which the rabbis refer to as Oral Torah. For the rabbis to be correct in regard to anyone born of a Jewish mother who accepts Yeshua as the Messiah then Jewish people must conclude that the rabbis have been given their authority by God and therefore the rabbis think like God and express God’s will through the Talmud. If this is true Jewish people should be able to find this transference of authority in the Tenakh. What we do know is that the rabbis changed the practice of Judaism after the destruction of the first Temple in 586 BCE. After they returned from Babylonian captivity and rebuilt the Temple they returned to Temple rights. With the destruction of the second Temple in 70 CE the rabbis once again reverted to an alternative Judaism which became rabbinical Judaism or Torah Judaism as the orthodox refer to it. Where did God give the rabbis the right to adhere to this alternative form of Judaism where they abrogate the words of Moses in Lev. 17:11 concerning the shedding of blood for the remission of sins? Furthermore; where are Jewish people promised eternal life in the Torah if they fail to keep all 613 laws? Where do we find this in the Tenakh? All Jews have failed to keep all 613 laws blamelessly. (See Pro.16:2, Ecc.7:20, 1Kings 8:46, Isa.59:1-2, Isa.1:18, Isa.64:6, Ezek. 18:30) The Jews who believe in Yeshua asked these questions and do NOT find any mention of the “oral torah” in the written Torah nor do they find it anywhere in the Tenakh. So they questioned the authority that the rabbis gave themselves. In examining their scriptures in the Tenakh they conclude that the messianic picture painted in the Tenakh is of the Jew Yeshua as portrayed in the New Covenant scriptures. These Jews who have made this decision worship Yahveh through Messiah Yeshua according to the Tenakh in a synagogue. Their decision is a matter of conscience since they do not find in their scriptures where Yahveh has given the rabbis the authority to determine who is a Jew. So the rabbis reject these sons and daughters of Jewish mothers because these Jews reject the rabbinical claim and accept the claim of Yeshua that through acceptance of his Passover passion, death, and resurrection both Jews and non-Jews can be reconciled to a Holy and Just God. Therefore those who accept Yeshua and come from a Jewish background are saved through the grace of God and will forever be Yehuda (a praise to Yahveh)—Jews.