I've heard this statement made many times by Christian missionaries that there is a Chapter in the Bible that Jews have been forbidden to recite.

Really?

 

This is very dishonest, first of all there are many portions of not just Sefer Yeshayahu (Isaiah) but within the books of the other prophets that we skip during the Haftarot yearly and not just Yeshayahu 53..
And only someone not familiar with Judaism would think that Jews read the prophets straight through yearly in the synagogue.. (The order is all over the writings of the prophets ie not in order)
Christian Missionaries would also be surprised to know that halachachicly there is NO set order of Haftarot (Prophetical readings) that have to be read,


In other words the practice was just to read (ANY) portion of the Prophets to fulfill ones halachic obligation.

Missionaries should first stop and verify their sources before just parroting what another missionary may of said, because if they did they would know that no where does an order exist in talmudic literature for the order of the Haftorot and not even for the Parashiot (weekly Torah segments) as we have them today....

In other words where do they get the idea that IS 53 was read and then later forbidden? No where... very dishonest....
In other words any Jew could read it (IS 53) today if he likes on Shabbat and not be violating any law, however our obligation is to chose a portion of the prophets that ties into the Torah portion read that week.
(Can you think of a Torah portion Yeshayahu 53 ties into, especially if you think its about Moshaich being that the concept doesn't literally appear in Torah.)

 

The order of the Haftorot that we have today was developed much later almost 1000 years later just to organize the Shabbat service a bit, and as you know that many communities also have huge variations in their Haftorot liturgy...
To end
(According the contextual meaning) (Rabbinic Mysticism aside)
Isaiah 53 and the whole suffering servant songs are speaking about Isaiah and every prophet that came before and after that was made to suffer when Hashem sent then to unrepentant Israel.
Being that many prophets were also anointed with oil then they would also be considered messiahs) but not one guy ie JC...

 

R' Asher Meza