In 1973, I got involved with a church on Hicksville, Long Island called St. John's Lutheran church. It had a sister church, Christ Lutheran, in East Meadow.
At first, there was a minimally Jewish orientation. A number of Jews belonged to this church including some people who went to my synagogue's Hebrew school.
About a year after I joined it, the leader, Jack Hickman, decided to reform the church. It's a very long story and I plan on putting a document about it up on my site at
groups.yahoo.com/group/exharedimsite.
This church went so far as to keep orthodox Jewish laws like Nidah, Negiyah, Kashrus, etc. It built a mikveh, a bimah and an Aron Hakodesh, and bought a Sefer Torah.
Today, "Messianic Jewish" congregations are all over the place but I belonged to one of the first. I found that it simply led me to more trouble than I already had.
My father enlisted the aid of the Lubavitch to get me out, but it backfired and I got more entrenched as I left my parent's house the day before my 18th birthday to live with members of the church which was now a full blown cult.

When I got involved in Jack Hickman's organization, it was billed as "your church". There were free dinners, lots of fellowship, free bible studies, etc. Then about a year later all of a sudden that deal was off.
The membership was divided up between 12 elders and each member of the church was assigned an elder to oversee his spiritual development. Mine was fellow "Hebrew Christian" named Bob Gross.
An inner circle was created in the church, called "the Family" and Jack Hickman, now taking on the name of Jacob Abensur
(after the family of kabbalists) was the "Abba" or father of the church.
Pretty soon, guards were patroling the church, now a full blown cult. I know of one member who was beaten up by the elders for some reason I forgot.
The Lubavitch were called in to fight the church and other religious organizations, like the local Catholic Church's got involved.
Hickman was eventually confronted with his homosexuality and his lack of Jewish ancestry (his mother was called up in Portland, Oregon. She said her son was "a very sick man".)
The people who owned the deed to the church and the deed to Hickman's house revoked the deeds and threw him out.
A relatively new phenomenon back then, now there are many Hebrew Christians. Some of these congregations don't keep the laws of the Torah according to orthodox standards and some do.
In Israel, there are a number of these churches which keep the othodox laws of Kashrut, Nidah, Negiya etc.

Awhile back I was near a pert, young woman who was obviously from some Christian congregation. I've seen her look before.
All of a sudden, she mentioned something about the "ancient Israelites" and looking at me, started to laugh. This was a Note worthy happening to me.
My experience with some Christian groups is that they think that my ancient ancestors were on the right path, but Jews today are not. Basically, all our religious experiences and struggles are invalidated after Jesus.
The church I went to claimed that the "true Jews" were the Sephardim (Jews from Arabic countries and Spain) and not the Ashkenazim (Jews from Eastern Europe). And Jack Hickman claimed descendancy from the Abensur and Abulafia clans, a family of Kabbalists of Sephardic origin.
I'd like to ask these people what leads them to believe that either the ancient Israelites or Maimonides (he was from Spain) wouldn't find them strange.
A bearded ancient Israelite who didn't know from indoor plumbing would probably have seemed very strange to this Christian woman. And he to her, had they met.

If you peruse the web, you'll find loads of these so-called Messianic Jewish sites. Just how many Jews run them and just how many Jews actually belong is a mystery but I'd guess not many.

My father told me that years ago, in England, where my grandfather is from, the church tried to convert just one Jew at a time spending millions in the process. And no one converted. Now, about 100K or so Messianic Jews are in existance.
All through the ages very few Jews converted, but those who did very often became a sore spot on the Jews. New converts are often the worst.

There's a bookstore over by the Jaffa Gate in Jerusalem that tries to convert Jews openly. The missionaries take on Hebrew names and tell potential converts how to "complete" their Judaism. For example, there's 2 types of Jews, a completed one and one who hasn't [found the truth].
Also, Israel attracts missionary groups that put on musical performances et al. on the streets of Jerusalem both in the old and new city.
This time of year, the Yomim Noraim (days of awe) tends to attract more activity as missionaries up the pace of trying to convert Jews.

If I remember correctly, it's illegal for churches to try to convert Jews in Israel.