In my opinion, according to the Bible, they are not Christians. They still live in the old covenant, they circumcise themselves, they celebrate the Sabbath and they also keep other laws of Moses. They still live like a servant of God although the new covenant has made Christians children of God. They try to keep the law even though it is not possible. Many Messianic Jews do not even believe that Jesus is God. The funny thing is, some Messianic Jews themselves admit they are not Christians.
They believe Jesus, their "messiah," died for their sins, rose from the dead, and will come again. That makes them a form of Christians.
At the very best, they are a synchronistic religion, meaning that they combine two religions, Christianity and Judaism. And that is only some of them. You see, MJ's are not a united bunch. The only thing they really agree on is that Jesus is the messiah and that it is okay to keep the law. Everything else is up for grabs.
But you do have those occasional MJ congregations that do keep the Torah, even some that keep the Torah and give weight to the Oral Torah (see the Messianic Jewish Rabbinical Council). I think we must admit that these few are indeed influenced by Judaism as well as by Christianity. Interestingly, it is this branch of MJ which discourages non-Jews from attending their services unless they are intermarried, and actually has majorities of Jews. Mark Kinzer, in "Post Missionary Messianic Judaism" argues fervently that MJ is a Judaism. I would disagree with him most strongly. But I would acknowledge that his brand of MJ is indeed synchronistic.