Along with the influx of Ukrainian war refugees seeking a safe haven through the Law of Return, Israel is absorbing many Russian immigrants who also seek to escape the war.
"We were the next on the list," the couple told their story in their borrowed flat in Rehovot, a quiet city 20 kilometers (12 miles) south of Tel Aviv.
Once you're on the list of alleged "foreign agents", you face a life of "self-censorship or, sooner or later, prison", said Bogolyubov, who directed the German-financed 2019 documentary "Town of Glory".
The film portrays President Vladimir Putin's use of references related to the fight against Nazi Germany to establish his authority in Russian villages.
As its international isolation has deepened, Moscow has come to view all movies made with foreign financing with suspicion, including documentaries, and the couple said theirs was no exception.
"Over the past few years, we felt threatened. In the past few months in particular, people were spying on us and taking photographs on our film sets," Shishova-Bogolyubova said.
The couple decided to continue working in Russia but, taking advantage of their Jewish ancestry, they obtained Israeli citizenship just in case.
Israel's Law of Return gives the right of citizenship to anyone with at least one Jewish grandparent, a criterion that tens of thousands in both Russia and Ukraine meet.
Opposition to war
Since Russian troops invaded on February 24, nearly 24,000 Ukrainians have fled to Israel, some but not all taking advantage of the law, according to immigration ministry figures.
They have been joined by around 10,000 Russians, an Israeli immigration official said.
"Most of those are young graduates, from the urban middle class," the official said, asking not to be identified.
Like the Bogolyubovs, Moscow-born linguist Olga Romanova had prepared for the day when she no longer felt safe in Russia.
She applied for an Israeli passport after Putin's annexation of the Crimean Peninsula in 2014.
"I always thought that one day I would join my children in Israel, but it was then that I realized that things were going wrong in Russia," the 69-year shared in her son's house outside Jerusalem, surrounded by photographs of her grandchildren.
When the invasion started on the morning of February 24, "it was proof that I needed to leave as quickly as possible.
"The war in Ukraine is incompatible with my way of thinking and my moral values. It makes me sick," she said, fighting back the tears.
New home or stopover?
The wave of immigration from Ukraine and Russia over the past seven weeks is the largest Israel has seen since the early 1990s when the collapse of the Soviet Union prompted hundreds of thousands to seek a new life on the shores of the Mediterranean.
"Here, we feel safe and we can sleep peacefully once more," said Shishova-Bogolyubova.
"My four-year-old daughter, who is diabetic, is completely taken care of.
"But we don't know if we will stay -- that depends on our work. Right now, we just want to live for the moment and recover from our emotions. Afterwards, we will see."
Sergey, a violinist who asked to be referred to by a pseudonym for fear of retribution, left Moscow for Israel with his pianist wife and three young children but expects to move on.
"I don't know if we'll stay here. We'll probably go somewhere else," he said.
Even for those who qualify for citizenship, Israel can be a terra incognita for new arrivals and nostalgia for Russia is never far below the surface.
Romanova, the linguist, found space in her 20 kilograms (44 pounds) of luggage for just two books, one an academic work, the other a novel by famed Russian novelist Mikhail Bulgakov which always accompanies her on her travels.
"I lost my country. It was stolen from me. It was taken by Putin and those KGB thugs," she said wistfully