Me, Litvish? Not now nor ever in my life have I ever been Litvish. Perish the thought, I actually like to be happy and joyous. I'll take the teachings of the Baal Shem Tov over any Misnagdim sect. In fact I don't consider myself involved in any group.
But I am in California. Other than Los Angeles there is pretty much no big Jewish communities. Thus I happily go to my local Chabad in my small city. And I have a soft spot for Chabad, and a deep love for the Rebbe. (Which I just bought one of his books "The Essence of Chassidut" on a trip to NY last week). In any event, I have heard from people statements from Chabad rabbis who say "Chabad does not do conversions". Of course this is not always true and may be a personal thing from each individual rabbi since Chabad is very open to all honest people. I have personally seen many Chabad rabbis who will help someone who honestly and sincerely has a spark and deep longing to go through giyur. The aversion some Chabad rabbis may have to become involved in the conversion process is the same as any other rabbi would have. Some are willing to help, some are not. It applies to any rabbi of any sect. All sincere Chabad converts would obviously be without a doubt hallahicaly Jewish, no argument there! And Chabad always says that no matter what a convert does they are always considered Jews (yes even Y-Love)- while other groups are quick to want to void the conversion all together. Chabad is the "good guy" in this case. When it comes to Yechi converts, I too have read cases of them being rejected by the chief rabbinate but I have not followed too much on it.
Nevertheless, I am keenly aware of the VERY limited list of who Israel will accept for aliyah. Keep in mind that it was recently (from 2006-2010) did Israel make news when they actively started to keenly reject many Orthodox rabbis and conversions for aliyah and came up with the list of what converting rabbis they would accept. This list caused quite a shock in the orthodox world because suddenly, rabbis who had performed conversions were told that the Israeli Interior Ministry and Chief Rabbinate would no longer accept their conversions. Or at least, the convert's Jewishness can come under suspicion at any given moment. It is a shameful situation when it comes to honest and good people who feel a passion to live a Torah life. To study and do a conversion only to be turned away. While everything comes from Hashem, hopefully the question (and sometimes injustice some legitimate converts experience by being rejected) may become resolved soon. On the other hand, while some people may be deeply hurt by the type of rejection, Israel has successfully rejected many African immigrants who try to open conversion files. Also, stopping many insincere and dishonest people who try to do conversions merely to live in Israel, marry a Jew (converting only for marriage) and for economical purposes.
I am not aware of the Badatz of Crown Heights continuing being on the list of the Chief Rabbiate/Interior Ministry since I had not seem them on there. I apologize for not taking them into consideration. It is possible that the current published list is not completly updated to include them. It may not have all approved batei din on the list. Maybe it only lists some but that is why there is also a number, to call and see which others ones are not on the list.
Here is the current list:
http://www.itim.org.il/eng/?CategoryID=208&ArticleID=209 (http://www.itim.org.il/eng/?CategoryID=208&ArticleID=209)
The Israeli rabbinate recognizes only Orthodox conversions performed by a bet din (rabbinical court) that appears on its list of recognized rabbinical courts.
Here is an example of the list:
California: Los Angeles Rabbinical Council of California: Rabbi Avrohom Union. Beth Din of Beverly Hills: Rabbi Gavriel Cohen/Rabbi Avraham Teichman. Beth Midrash Mishkan Israel: Rabbi Shmuel Ohana
New York: Manhattan Beth Din for Conversions: Rabbi Zvi Romm. Rabbinical Alliance of America: Rabbi Hershel Kurzrock. Beth Din of Agudath Harabbonim: Rabbi Aryeh Ralbag, Sepharadic Beth Din of Queens:Rabbi Eliyahu Ben-Haim/ Rabbi Menachem Zilber. Monsey Rabbi S.J. Landesman
Of course, to confirm that a beis din is on the list of the Israeli chief rabbinate, one can call them in Israel directly to verify the list.
Other than that, the following are just examples of articles I based my comments on:
A 2006 article of when the barring started: http://www.itim.org.il/_Uploads/dbsAttachedFiles/Jewishweek5.5.06-ChiefRabbinateBarringConversions.pdf (http://www.itim.org.il/_Uploads/dbsAttachedFiles/Jewishweek5.5.06-ChiefRabbinateBarringConversions.pdf)
A 2011 article: http://www.haaretz.com/weekend/anglo-file/american-rabbi-hopes-new-guidelines-will-change-rabbinate-s-stance-on-conversions-1.351689 (http://www.haaretz.com/weekend/anglo-file/american-rabbi-hopes-new-guidelines-will-change-rabbinate-s-stance-on-conversions-1.351689)
Currently, the Israeli Rabbinate only accepts conversions by a limited number of Diaspora rabbis, and at least 10 Orthodox converts who went through other rabbis were denied Israeli citizenship based on the Rabbinate's recommendation in the past few months.
For Reform or Conservative converts, the ministry relies on the Israeli branches of these streams. In the absence of a central body representing Orthodoxy, the ministry started turning to the Rabbinate regarding the validity of Orthodox conversions. The Rabbinate, however, only recognizes a limited number of foreign conversion courts.
Sephardi Chief Rabbi Shlomo Amar spoke of people who paid high sums for conversion certificates from Orthodox rabbis in the U.S. To avoid such frauds, he said, he would only accept conversions conducted by the rabbis on his list. The full list has never been publicized but includes 12 conversion courts established by the Rabbinical Council of America, or RCA.
Another recent 2011 article: http://www.jpost.com/JewishWorld/JewishNews/Article.aspx?id=207794 (http://www.jpost.com/JewishWorld/JewishNews/Article.aspx?id=207794)
At the same time, while non-Orthodox conversions conducted in courts recognized by the Israeli leadership of the Reform and Masorti (Conservative) movements are not recognized by the Chief Rabbinate as valid Jewish conversions, the State of Israel sees these converts as Jewish and grants them citizenship
when Canada native Thomas Dolhan applied for aliya a short while ago, he was informed that his Orthodox conversion – conducted by a court composed of two rabbis from the International Rabbinic Fellowship (IRF) and one from the Rabbinical Council of America (RCA) – was not valid.