Is there any Christian group that takes Matthew 23:8-10 literally?

It's not exactly a group.

Christianity Today Article Organic Church not exactly a movement

You will find references to Matthew 23:10 in the following: Making Disciple Makers

Quote

Spiritual fathering – a relationship

All mature believers ought to aspire to be a spiritual father (parent) in the Lord by virtue of relationship and/or stature irrespective of call and grace gifting. Of course, we would only be wise to follow the teachings of Christ and avoid corrupting this precious relationship by turning it into a position or title (Matthew 23:8-10). Thus Billy Graham, for example, would be seen as a father in the Body of Christ. His equipping gift of evangelist has, along with his integrity over many years, given him this platform. But his fatherhood is irrespective of the gift he has. This would also be true of many, many less well-known men and women of God; their fatherhood, gender-neutral of course, is based on their relationship with others and the godly esteem they are held in.

Matthew 23:9 must be understood in the traditional Jewish cultural and religious context.

Students (talmidim) would often refer to their teachers by various titles that indicated significant esteem. These titles included רב (Rav), רבי (Rabbi), מר (Mar), and אבא (Abba). This translate into English as "great one," "my great one," "lord," and "father," respectively.

• מר (Mar)

Marcus Jastrow: A Dictionary of the Targumim, the Talmud Babli and Yerushalmi, and the Midrashic Literature, p. 834.

Example: Babylonian Talmud, Seder Nezikin, Tractate Sanhedrin, Chapter 11, Folio 94a (English/ Hebrew)

Where did he deport them to? Mar Zutra said, "To Africa." Rabbi Chanina said, "To the mountains of Salug."

להיכא אגלי להו מר זוטרא אמר לאפריקי ורבי חנינא אמר להרי סלוג

• רבי (Rabbi)

Marcus Jastrow: A Dictionary of the Targumim, the Talmud Babli and Yerushalmi, and the Midrashic Literature, p. 1442.

Example: Babylonian Talmud, Seder Nezikin, Tractate Sanhedrin, Chapter 11, Folio 94a (English/ Hebrew)

Where did he deport them to? Mar Zutra said, "To Africa." Rabbi Chanina said, "To the mountains of Salug."

להיכא אגלי להו מר זוטרא אמר לאפריקי ורבי חנינא אמר להרי סלוג

• Hebrew רב (Rav); Aramaic רבא (Raba)

Marcus Jastrow: A Dictionary of the Targumim, the Talmud Babli and Yerushalmi, and the Midrashic Literature, p. 1438.

Example: Babylonian Talmud, Seder Mo'ed, Tractate Pesachim, Chapter 9, Folio 92b (English/ Hebrew)

Rav Nachman said, "It is accepted." Rav Sheshet said, "It is not accepted."

רב** ששת אמר לא הורצה רב נחמן אמר הורצה**

Example: Babylonian Talmud, Seder Zera'im, Tractate Brakhot, Chapter 1, Folio 3b (English/ Hebrew)

But Raba said, "There are two kinds of neshef: when the evening disappears and the morning arrives; when the day disappears and the evening arrives.

אלא אמר רבא תרי נשפי הוו נשף ליליא ואתי יממא נשף יממא ואתי ליליא

There are a few others, but I believe this demonstrates the context sufficiently.

Edit: To clarify, there is no reason you may not call your own biological father, "father." It is stated in both the OT and the NT that we are to "honor your mother and father."

The issue concerns calling those in positions of authority (especially religious) by titles of esteem, especially those in the Church. Yeshu'a said that those who were great and first among us were to be our ministers and servants (cp. Matt. 20:26-27). A master does not call his servant, "lord"; likewise, we should not call those who serve us by such titles. For example, "Papa" for the Pope, "Father" for priests, "Rabbi" for Jewish teachers. These are exactly what Yeshu'a was referring to. In addition, to think that he told his disciples that they were not to call the Jewish religious leaders Rav, Rabbi, Mar, Abba, etc., but then Gentile believers can call their religious leaders, "Pope," "Father," is simply nonsensical.

The entire premise behind this prohibition is that there is one alone deserving of esteem, and that is our Lord (Master). All those who believe in him are his servants.