The Ten Commandments are all reiterated in the New Testament, page-33

"On a related issue.
There are mind-bending varieties of ways of seeing what the NT portrays among Christians.
How is this explained to Jews when saying that the OT is a forerunner of the NT?"

Re your second line -> You have correctly noticed this and this should make all Christian's stand to attention and open their eyes and ask WHY, as due to quite a number of messages in the NT, if people were on truth, this should not be possible, unless you assume the Father and Son failed, or lied.
Based on messages, no if buts or maybe's, what you say should be expected, as I see it.

In short, the Bible theme is centered around mind games, a play on words = messages - interpretations and according to Gen's, it began there.
The Bible says, there is nothing new under the sun, what was will be.
It also says, God reveals the end from the beginning, so if we go back to near the beginning, deception, lies began and if we reverse that to the end, it suggests deception and lies, right up to near the end.
From what I see, this is running true to form.
(And yes, there are other reasons for - end revealed from the beginning).

(As I see it, the opposition would concentrate on deceiving within Christianity, the Muslims would already be deemed as a Checkmate matter, so leave well alone lol.
I feel the wolf in sheep's clothing, has grossly been underestimated).

What it will amount to though, I'm not sure as I'm not the judge, but many verses suggest it is not good, or at the very least, serious tough times will come to many, which they will have to endure, as I expect truth will be revealed just prior to these tough times (wrath, not tribulation, which was before), but you have missed the boat, so to speak to be taken out of harms way???
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"How is this explained to the Jews" -> Imo, due to the mainstream Christian followings, I suggest that perhaps in a big way, the mainstream following, is possibly a substantial factor, contributor, in why many Jews will not accept that Jesus has come.

One example, just take one OT quote that the Jew would cling to -> Hear, Israel: Yehowah our God is ONE Yehowah = no way can you say this One consists of 3 persons.
All through the OT, God is constantly wanting people to know him and worship the True God.
If he was 3 persons, worshiping a singular person, would be deemed as worshiping another God.
Hence, imo, no way would God allow this to go on, without clearing this matter up -> allow it to go on for 4,000 years, hmmm, I DON'T think so.

(I didn't mention this, to create a trinity debate, just coming from a Jew perspective and how could the True God, suddenly become 3 persons ).
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"They have an alternative explanation for the forerunners based entirely on the OT."

I've not examined the who's and whys as to why the Jews say the OT doesn't align with the NT.
But I expect you will find, many literal and physical events in the OT, will align with the NT, but in a Spiritual context.
Ex - Jesus is ruling now as King and it appears that this began when he was seated at the RHS of God.
(Us being in what you might say is, stage 2 of 3).

However, it appears many of the mainstream Christians think that no, this happens when he comes and rules for a literal 1,000 year period.
I think they call that, futurism.
However, the Greek word for the 1,000 = plural - thousand - thousand = simply a long period of time and not a one of 1,000. (that's what it appears?)

It appears, that this is part of a deception ploy, just as many falsely believe that the Bible teaches, a literal 3rd Temple, when it does not.
The verse they draw upon, the same writer at least 3 times elsewhere, says People are now the Temple, but they so no, he doesn't mean that in the other verse = Ya WHAT???????? LOL.
However, one may go ahead, to fulfill or continue the deception.
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On a closing note and possibly off track -> I'm of the opinion that when end times come (whether I'm alive or not lol?), the deceptions in the world will be revealed and they will be way beyond what our minds could've imagined and I'm not just talking about Christianity here.
The latest line being thrown out there atm and picking up speed, the moment someone mentions something that is considered not the norm, the conspiracy card is thrown at them.
Unfortunately, real conspiracies are thrown out there, which are probably created to counter some truths, to give them the brand of conspiracy.

A bit like the counter reformation porkies thrown out there, which it appears, are Huge in number.