I wonder if this sort of thing happened often during the Soviet era. While I know there was no religion allowed during that time, were muslims able to attack the USSR with the type of impunity they enjoy in this day and age?
The Soviet Union was always a regime of oppression. Differences were in the degree in which things were enforced. To answer your question directly, any kind of clandestine activity, even without use of arms, would be automatically suppressed. But, of course, even in the Soviet Union murders happened, including murders committed with (forbidden except for servicemen and hunter long-arm) firearms.
Religion as a private activity was allowed. A few paces of worship were allowed to exist, but hardly ever new ones were allowed to be built. There were Christian churches, predominantly Orthodox, mosques and synagogues that operated — not enough to cover the true needs but in some measure. The Orthodox Church was treated better than other confessions, except in the early days after the Bolshevik Revolution, when it resisted the Reds.
Outspoken priests existed all along. I had the privilege of knowing Fr. Men’, who was also murdered, for motives unknown. The authority tolerated purely religious teaching especially so long as it was oral during sermons. Whatever went into the cultural or political arena was treated with suspicion, and if it could not be controlled, either suppressed by law enforcement or some accident would be arranged to silence the dissident.
I know little about Islam in the Soviet Union. The traditionally Muslim population was large and quite docile. I never heard of any Muslim extremism or dissident mullahs, but then I never lived in those areas. The radicalization of the Muslims of the former Soviet Union happened after the USSR broke apart.