I did not expect to be able to answer this one!

I believe the person who identified it in the other thread as the funeral of Rabbi Moshe (Moses) Feinstein, a leading Orthodox rabbi, one of the most prominent decisors of Jewish law in modern times, and head of the yeshiva Mesivtha Tifereth Jerusalem, is correct, and it was my first thought on seeing the photo. It fits with

• the location- East Broadway has been the location of his yeshiva for many years
• the timing- he died in 1986, which fits in the timeline, and coincidentally, his 33rd yohrzeit (anniversary of his death) is this Wednesday according to the Jewish calendar
• the apparently heavily male crowd- among Orthodox Jews it would be far more common for men to be part of a funeral procession of this kind, and he was the rosh yeshiva [headmaster] of a yeshiva for men)
• the garb of many of the men in the photo- if you look closely at the men on the left side of the barricade, the only place where individuals can be clearly made out, they seem to be wearing black suits with white shirts (which is common in general at Western funerals) but also no ties and black hats (much more specific to right-wing Orthodox Jews of the kind that Rabbi Feinstein was). I think I MIGHT see some beards but I can't tell, which would also be a clue
• the vast numbers of people- attendees at the New York were in the tens of thousands, reaching the hundreds of thousands if one includes the attendees at the Jerusalem funeral shortly after (where he was buried)

As far as why a funeral would be in the middle of the street, the concept of halvayat hamet (accompanying the dead) is a highly significant one in Judaism, and walking with the coffin from the location of the funeral service to the cemetery is extremely common, or at least walking with it until the hearse. This is even more common with the funerals of great rabbis, which, as in the case of this funeral, can attract massive throngs. (There was actually a funeral of a great rabbi in Israel a few years ago, which I believe attracted upwards of 100k people, in which a man was trampled to death as part of the crowd- it was horrible.) Since these funerals attract so many people, they can't possibly fit inside the location of the funeral service (in this case the yeshiva- my father did attend the service at the yeshiva, and said it was extraordinarily crowded), generally the rest of the mourners will stand outside and listen to the eulogies on a loudspeaker, or these days via video hookup. This is also helpful for kohanim (Jews who descend from the priestly class), who are forbidden according to Jewish law from being in the same room as a dead body- the kohanim were able to participate from outside.

Also notable is the fact that UPI apparently printed a story about it, which would explain how your friend got the photo. (That said, they got some details wrong- he had two daughters named Faya Gittel and Shifra, not one daughter named Faya Shifra, for example.)

On a personal level, I'm especially thrilled I saw this as my family has a personal connection with Rabbi Feinstein (or R Moshe, as he is known among many in the Orthodox Jewish community)- my grandfather attended his yeshiva for many years and received rabbinic ordination from him, and stayed close with him for many years afterward. In general, also, it's hard to overstate how incredibly highly regarded Rabbi Feinstein is and was in the Orthodox Jewish community as a rabbi and decisor of halacha (Jewish law). To this day, he is considered one of the greatest rabbis of the modern era, and was even respected on a personal level (even if they didn't at all see eye to eye) by rabbis from other Jewish denominations. Especially to see this the week of his yohrzeit is really meaningful to me.