There are other allowed religions if state has state religions. Did Romans tolerate Christianity when Emperor worship was state religion?Being direct won't hurt my feelings.
I don't want to invent an answer for the existence of mosques in Russia. I don't know enough about Islam and how it functions under different governments to knowledgeably say for certain. Maybe they are also useful to the government.
However, that article you linked to said that this building was rebuilt as a historical monument by the President of Tartarstan.
Tartarstan is described thusly: "After hundreds of years under Russian rule, the Tatars are now well integrated into Russian society. However, they continue to maintain a distinct culture, characterized by their Islamic faith and native Turkic language."
"The Volga Tatars, also known as Volga-Ural Tatars or simply Tatars (Tatar: татарлар, romanized: tatarlar; Russian: татары, romanized: tatary) are a Turkic ethnic group native to the Volga-Ural region of western Russia, and contains multiple subgroups. Tatars are the second-largest ethnic group in Russia after ethnic Russians. They are primarily found in Tatarstan, where they make up 53.6% of the population. Their native language is Tatar, and are primarily followers of Sunni Islam."
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Volga Tatars - Wikipedia
en.wikipedia.org
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Federal subjects of Russia - Wikipedia
en.wikipedia.org
So they don't really sound like they are culturally Russian, but more like an attached governed body.
This is my source for my explanation of the Cold War (potential) strategy of the KGB:
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New Lies For Old: The Communist Strategy of Deception and Disinformation : Anatoliy Golitsyn : Free Download, Borrow, and Streaming : Internet Archive
A former KGB officer provides a revealing look at Soviet policy and objectives and explains how the Communist use of political deception and disinformation...archive.org
That's point. I choose Muslim since it's easier to prove they exist and therefore Russia doesn't have state religion.
Now Orthodoxy may have big influence of state and law, but that does mean it's Russian state religion.
Regarding KBG's strategy, your problem isn't proving it was then strategy. Maybe yes, maybe not. Real issue is it now same strategy?
West has it's own homebrewed (woke) Communist, you maybe Russia ones aren't problem. Did you take into account Chinese Communists?
CCP is still officially Marxist-Leninists party and Chinese were caught several times trying to biological damage makers (fungus etc... damaging to crop). Maybe they are real issue.
Upsss, I forgot, some bigwig (Neville Roy Singham) with CCP connections is financier of Democrat party.