Given those two religions tend to bury their deceased rather quickly.
GHW Bush died on Friday. His remains are being transferred today (Monday) to Washington D.C. where they will lie in state in the US Capital from this evening until Wed morning. Following a funeral at the National Cathedral he will be flown back to Houston to lie in repose overnight before finally traveling to the cemetery on Thursday for burial.
How would the public get to pay their respects?
I suspect they have no idea because it’s not close to being an issue yet. Plans for each president are already in place. The presidents themselves have a large say as to how the procedures will go. Until there is a Jewish or Muslim president there is no way to know their individual wishes.
Does there need to be a corpse in order for “the public to pay their respects”?
What happens if we have a president who dies from falling into a volcano, or something like that where we don’t have a body?
If a US President died by falling into a volcano, that would be proof that we are living in an action movie. By the laws of action movies, no body means the president is actually alive, possibly recuperating from a devastating wound and definitely training so that when he returns he can handily defeat whichever foe tossed him into a volcano and save our nation.
“Sorry, Dr. Vulkan! It looks your plot to set off the Yellowstone Supervolcano and destroy America has just been… VETOED!”
When Yitzhak Rabin was assassinated, he was buried 2 days later with many global leaders in attendance. I’m not sure why it would be different in the US, assuming the public service is led by competent people that have established plans.
Your application for asylum has just been REVOKED!
Is this a plug for Joe Biden vs the Volcano?
We could ask the Australians - they lost a sitting Prime Minister when he decided to go for an impromptu swim in a coast known for its dangerous and unpredictable tides: Harold Holt.
Don’t worry, and I’m saying this as a Jewish person, an Alien from space will be elected President before this country ever elects a Jewish person President.
That’s true. And when King Hussein of Jordan died, all the world’s leaders showed up, too, even though he was buried the next day. (Including the current US president and a couple of past-presidents.) Admittedly, his death was expected, but still, it can be done.
As for the rest of the public, Jews often hold memorial services a few weeks after the funeral. You don’t need a preserved body to show respect.
I don’t believe that at all. Michael Bloomberg and Al Franken stood excellent chances of being elected President.
Yeah. It’s like the crazy idea that a black guy would ever be president. Nuts, right? 
The only reason I see that a Jewish person or a Muslim (or an Asian) wouldn’t be elected is, simply, not many actually run for office. They are a pretty small minority of the population, overall. Other than that, I don’t think their religion would be any more of a bar than Obama’s skin color was.
As to the OP, I don’t see the issue. There is a whole staff that is dedicated to looking into protocol stuff like that. If/when it’s an issue they will handle it the same way they handle stuff like Bush’s recent death.
While officially Episcopal, National Cathedral is open to other religions. My daughter saw the Dalai Lama preach there when she lived in DC.
It would depend on the wishes of the deceased, but the Cathedral itself would have no issues holding Jewish or Muslim services.
My recollection from evangelical Sunday School lessons is that the correct answer is “they go straight to Hell.”
And you know how nutty their burial customs are!
I’ve been to Jewish services in a church. They draped a banner over the cross. The banner said, “how beautiful it is when brothers dwell together in unity” (in Hebrew – from psalm 133 – it’s a popular song at Jewish services.). It’s just a building. That particular building was in Manhattan, so I suppose it was efficient to use it for a big congregation both Saturday and Sunday every week.
I’d expect a non-Christian president (or his survivors, if the death was really unexpected) to pick a secular location, but there is no shortage of those in the DC area.
And Jews are significantly over-represented in Congress.
You ought to write for film! I can see that scene playing in my head.
A local Episcopla church did it the other way around. Their building was torched by an arsonist. A lot of local congregations offered worship space, but the most convenient, for Sunday morning worship, was the one synagogue in town. A nice spce designed for worship, and not in use on Sunday morning! All they asked was that when breakfast was served was that the sausage be turkey sausage, not pork.