Others have answered what the Jewish view of this passage is, I am just going to add the historical conntext of the jewish view to refute the false claims of the Christian missionaries that this is a modern view. Probably the moset effective counter tomissionaries is to show that the early Christians themselves were aware of the Jewish interpretation fo this as pertaining to the nation of Israel: Origen in the 3rd century and Justin martyr both stated that Jews believed this
There are also many anciemt Jewish sources: The Talmud in masechta Berachos relates Isaiah 53 to the nation of Israel, Midrash Rabba Bamidbar applies it to Israel as a nation, Midrash Rabba Devarim applies it to Israel, Tana Devei Eliyahu applies it to the nation of Israel, the Kuzari applies it to the nation of Israel, Chovavot Levavot applies it to the nation of Israel. Rashi applies it to Israel
The normal Christian claim is that Rashi was the first to utilise this claim- EVERY other source I hae listed above predates Rashi, most by centuries and some are based on oral traditions that go back to the time of the first Temple.
Of course, the Christian missionaries when misrepresenting Jewish sources to try and use them for missionary purposes don't acknowledge this- nor do they point out the fact that even where specific verses are applied to the Mashiach in Jewish sources- it is always SPECIFIC verses, never the passage as a whole, and in some cases it is a specific section of a verse. You will not find any Jewish source that refers to the entire chapter as talking about the Mashiach.
Lets look at one example of how the Jewish reference to Isaiah 53 in the Talmud is taken out of context. The reference we see missionaries using for this is Sanhedrin 98B- where a homilectic discussion around variuos names for the Mashiach are discussed (and the explanations for this discussion take pages since they clearly are not meant literally) The passage there goes:
What is his name? The school or R' Shela says "Shiloh is his name as it is stated, "until Shiloh comes""
The school of R' Yannai says "Yinon is his name, as it is stated "May his name endure forever, for as long asthe sun may his name continue"
The school of R' Chaninah says " Chaninah is his name as it is stated "For I will not give you mercy" and some Menachen ben Chiskia as it is sated "become a comforter to receive my spirit far from me" And the Rabbis say "etzora ofthe House of Rebbi is his name as it is stated "indeed it was our diseases that he bore and our pains that he endured, where as we considered him plagued, smitten by G-d and afflicted."
As can be seen, the verse only discusses a possible name for him, it does not refer to the life of the Mashiach or his attributes at all! After all, if we were talkign about a literal metzorah, we would be talking about somebody required to sequester himself and not to interact with anyone until he was healed, unable to enter the Temple, offer sacrifices etc- and such a person coul not be the Mashiach!
I also fond the reference to Isaiah 53:10 amusing:
י וַיהוָה חָפֵץ דַּכְּאוֹ, הֶחֱלִי--אִם-תָּשִׂים אָשָׁם נַפְשׁוֹ, יִרְאֶה זֶרַע יַאֲרִיךְ יָמִים; וְחֵפֶץ יְהוָה, בְּיָדוֹ יִצְלָח. And the Lord wished to crush him, He made him ill; if his soul makes itself restitution, he shall see children, he shall prolong his days, and God's purpose shall prosper in his hand.
Whats amusing about quoting this verse, is tbat it directly contradicts the Christian scriptures stating ", he shall see children, he shall prolong his days,"- Jesus died young and with no children, the opposite of what this verse states!
As for the claim that the chapter is avoided by Jews, that is most amusing. My Mikraot Gedolot (an edition of the Tanakh which contains around 29 commentaries across the various books of Nevi'im (prophets) and Ketuvim (Writings) has 17 different commentaries on this chapter (the majority of which are after the 11th century, supposedly when we started to ban the chapter lol). Quite difficult to comment on a chapter that you aren't reading lol
edit: hilarious, isn't it, how one of the "messianic jews" tries to misrepresent my answer and ignore the fact tha I am shoing that the quote from the Talmud is misrepresented by missionaries; and how he ignores all the sources posted that show Judaism do NOT see this chapter as talking about the Mashiach. ah well, I guess I will just have to thank him for giving such a great example fo how "messianic jews" misrepresent Jewish sources!
Orthodox Jew; acting Rabbi