@iwonderwhatif,
You have made a rather large assumption that the conflict between Middle Eastern Muslims and Israel is not existential.
The fact that since 1973 Israel has maintained essentially peaceful relations with all of its Muslim neighbor states, except Lebanon, would seem to suggest that political accommodation is possible, however the fact that Israel has, during this same time period, been engaged with no less that 7 extended armed conflicts with either Lebanon or the Palestinians strongly argues that it is not.
Israel does not have fundamental points of conflict with Lebanon and the Lebanese, and while there have never been diplomatic relations between the two countries, Lebanon was the first Arab League nation to approach Israel for a peace treaty in 1949 and didn't participate in either the 1967 or 1973 Arab -Israeli wars. Yet 4 of the 7 wars Israel has fought in since 1973 were with Lebanon.
These 4 wars may have involved fighting on Lebanese territory, but the Israeli's actual opponents were Syria and/or Iran who funded and directed Hezbollah
Setting aside whether or not the theocracy in Iran poses an existential threat to Israel on ideological grounds, clearly Iran has mid and long term goals for controlling the entire Middle East region. Israel has been and always will remain a threat to those goals. It is hard to imagine a scenario in which Iranian hegemony is established in the region and Israel remains a democratic, Jewish state. As long as Iran has designs on the region, political accommodation with Israel will not be possible. In addition, short of using military force, neither the Chinese nor the Russians will be able to persuade Iran to give up its imperial goal and reach an accommodation with Israel. The fact that Iran has been actively supporting Hamas in the second front of Israeli's wars since 1973 - Palestine, further demonstrates the extent to which Iran considers Israel a mortal enemy.
Syria has territorial disputes with Israel (Golan Heights in particular) and there is a long list of Syrian grievances towards Israel (including the recent destruction, by Israel, its developing nuclear weapons program) that would make it very difficult to effect an accommodation between the two nations. Add to this the fact that Syria has become a client state of Iran based, in part, on their shared animosity for Israel and it is clear that both countries represent implacable foes for Israel that the SCO would find extremely difficult to defang in any promises it made to the Israelis.
This addresses only Lebanon, arguably the easier of the two flashpoints to quell. Adding Palestine to the mix increases volatility by tenfold. While the expressed desire of Iran's leaders to wipe Israel off the map might be dismissed as posturing, the same cannot so easily be accomplished with the Palestinians and, in particular, Hamas.
Whether illegitimate or even deserved, the Palestinian grievances against Israel far exceed in intensity and consequence any that Syria or Iran may lay claim to. There is a legitimate reason to question whether or not Hamas will ever be prepared to offer Israel peaceful co-existence.
On the plus side for your proposal is the fact that the SCO would have a much easier time coercing the Palestinians than the Iranians or Syrians, but if Iran doesn't want an accommodation with Israel there is no reason to believe they wouldn't stand in Palestine's corner as respects the SCO.
As difficult as it would be to arrange an accommodation between Israel and its current regional foes, we haven't even asked the question, why would the SCO want to bother to try? From a resource standpoint they need the Arab nations and Iran a lot more than they need Israel, so why would they jeopardize relations with them to improve their relations with Israel?
It doesn't make sense, and kicking to the street the long time alliance between the US and Israel seems more of a symbolic than strategic goal.
One might argue that for China or the SCO to establish a broader hegemony in the region they need the US out of the picture, but if you are assuming that a collapse of the US economy would pave the way for this accommodation between SOC and Israel, the purpose of the accommodation can't be to rid the region of US influence, the economic collapse will have already accomplished it.
Admittedly it might offer the US some temporary geo-political relief to free itself of the diplomatic burden of close ties with Israel, but how does that compare with losing the entire region to Chinese and Russian control?
I see no chance of this coming to be and that is less because of religious and or historical hatreds, but because it doesn't suit the goals of most of the key players.