Mishneh Berurah   BaAl HaTanya   Aruch HaShulchan
  
Amongst the Rabbanim who support the use of soft Matza by Jews of all backgrounds, are -  
HaRav Y Sh Elyashiv more

HaRav Mordekhai Eliahu
Chief Rabbi of Israel

Rav Hershel Schachter more
Rosh Yeshivah RIETS Yeshivah University and senior Rabbinic authority at OU Kosher

Rav Aviner more
leader in the International Zionist Yeshivot

Rav Zev Weitman more
Chief Rabbi of the Tenuvah Dairy Corporation, Israel, the largest dairy business in the Middle East which is also Israel’s largest food manufacturer with a market coverage of approximately 70%.

Rav Chaim Twersky SEE
from      Chaim Twerski<chaimtw@gmail.com>
to          "Rabbi Meir G. Rabi, its Kosher!" <rabbi@itskosher.com.au>
date      Sun, Apr 10, 2011 at 1:22 PM

As I stated by phone, my involvement was minimal.  A sefardic Rav asked me permission to bake matzos in the factory for which I was the Rav HaMacshir. I gave persmission after having verified that even Ashkenazim are permitted to bake and eat  soft matzos and it is only a custom to eat hard matzos and not an halachic minhag. 

HaRav Mordekhai Eliahu
Mordechai Tzemach Eliyahu was a prominent Rabbi, Posek and spiritual leader. He served as the Sephardi Chief Rabbi of Israel from 1983 to 1993.
At the age of 31, he became the youngest person ever elected as a religious judge (dayan) in Israel. He served as the Chief Rabbi of Beersheba for four years, and was then elected to the Supreme Rabbinical Court in Jerusalem. He held the position of Chief Rabbi of Israel for 10 years.

Rabbi Hershel Schachter is Rosh Yeshiva at Rabbi Isaac Elchanan Theological Seminary (RIETS), Yeshiva University, in New York City. At the age of 22 he became an assistant to Rabbi Joseph Ber Soloveitchik, and at 26, he became the youngest Rosh Yeshiva at RIETS. At 30 years of age, was appointed Rosh Kollel, or dean of the Kollel. 
Rabbi Schachter is a well recognized and noted Talmudic scholar and a prominent Posek, he is also a Halakhic advisor for the Kashrut division of the Orthodox Union.
He is widely respected in the Yeshiva world as one of the Torah luminaries of the contemporary era, and for his close relationship with Rabbi Joseph Soloveitchik.

Rabbi Aviner was involved in the Bnei Akiva youth movement and rose to the position of National Director. Rabbi Aviner learned in the Mercaz HaRav yeshiva in Jerusalem, under Rabbi Zvi Yehuda Kook. He became the rabbi of kibbutz Lavi and later the rabbi of moshav Keshet in the Golan Heights. Since 1981 he has been the rabbi of Bet El. 
He is one of the leading rabbis of the religious national movement and is frequently called on to speak in public forums. He has published dozens of books: commentaries on Tanakh (Ruth, Ecclesiastes), Haggadah of Pesach, the works of Abraham Isaac Kook and Zvi Yehuda Kook and books about Orthodox Jewish morality and modesty.