NOt sure what muslims they talk about, but suni islamists will respect a strong secular government playing their games, instituting itself as their Kahlifate equivalent. Those in turn can become the most motivated troops of ruthless government.
You simply make these savage understand that the kufars and dhimmis who pay the islamics burden sins to islam first must pay the sins due of the state to the state, the state managing that. And then you make these muslims pay for the sins of the state too, bowing as they bowed to the Kahlif, turning the takfirism on themselves, hanging muslim neighbors who do not do the payment of state sins to the state in pious muslim manner.
Putin and Russians do not care if muslims rise in Russia, because they know how to keep them down with ruthlessness.
It is not referring to a rise in radical Islam, but to the number of people within Russias borders who identify as Muslim. I too have read from an article by demographic researcher Marlene Laruelle who says that a conservative estimate would be that Muslims are on track to make up 1/3 of Russias population by 2050. And alarmist estimates say 1/2.
This factors in citizens of Russias Islamic republics like Chechnya and Daghestan, but also the mass influx of Central Asian migrants from former USSR territories.
None of these estimates factor in things like Muslims who convert to Christianity, etc...
Public schools should teach us that incrementalism is the post WW2 method of choice to invade a nation.
I think you have the right idea. Authoritarians of various stripes can be symbiotic. Also the Islamic factions might look for the state to slap down the rival factions and the Russian state can play factions against each other.